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Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran
Autore Le Nam Q
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Descrizione fisica 1 online resource (VII, 228 p. 16 illus., 1 illus. in color.)
Disciplina 515.353
Collana Lecture Notes in Mathematics
Soggetto topico Partial differential equations
Calculus of variations
Differential geometry
Partial Differential Equations
Calculus of Variations and Optimal Control; Optimization
Differential Geometry
ISBN 3-319-54208-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Part I The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation and Related Linearized Monge-Ampère Equation -- Introduction -- Notation -- 1 The Affine Bernstein and Boundary Value Problems -- 1.1 The Affine Bernstein and Boundary Value Problems -- 1.1.1 Minimal Graph -- 1.1.2 Affine Maximal Graph -- 1.1.3 The Affine Bernstein Problem -- 1.1.4 Connection with the Constant Scalar Curvature Problem -- 1.1.5 The First Boundary Value Problem -- 1.1.6 The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation -- 1.1.7 Solvability of the Second Boundary Value Problem -- 1.2 Existence of Solution to the Second Boundary Value Problem -- 1.2.1 Existence of Solution via Degree Theory and A Priori Estimates -- 1.2.2 Several Boundary Regularity Results for Monge-Ampère and Linearized Monge-Ampère Equations -- 1.3 Proof of Global W4,p and C4,α Estimates -- 1.3.1 Test Functions -- 1.3.2 L1 Bound and Lower Bound on the Hessian Determinant -- 1.3.3 Gradient Bound -- 1.3.4 Legendre Transform and Upper Bound on Hessian Determinant -- References -- 2 The Linearized Monge-Ampère Equation -- 2.1 The Linearized Monge-Ampère Equation and Interior Regularity of Its Solution -- 2.1.1 The Linearized Monge-Ampère Equation -- 2.1.2 Linearized Monge-Ampère Equations in Contexts -- 2.1.3 Difficulties and Expected Regularity -- 2.1.4 Affine Invariance Property -- 2.1.5 Krylov-Safonov's Harnack Inequality -- 2.1.6 Harnack Inequality for the Linearized Monge-Ampère Equation -- 2.2 Interior Harnack and Hölder Estimates for Linearized Monge-Ampère -- 2.2.1 Proof of Caffarelli-Gutiérrez's Harnack Inequality -- 2.2.2 Proof of the Interior Hölder Estimates for the Inhomogeneous Linearized Monge-Ampère Equation -- 2.3 Global Hölder Estimates for the Linearized Monge-Ampère Equations.
2.3.1 Boundary Hölder Continuity for Solutions of Non-uniformly Elliptic Equations -- 2.3.2 Savin's Localization Theorem -- 2.3.3 Proof of Global Hölder Estimates for the Linearized Monge-Ampère Equation -- References -- 3 The Monge-Ampère Equation -- 3.1 Maximum Principles and Sections of the Monge-Ampère Equation -- 3.1.1 Basic Definitions -- 3.1.2 Examples and Properties of the Normal Mapping and the Monge-Ampère Measure -- 3.1.3 Maximum Principles -- 3.1.4 John's Lemma -- 3.1.5 Comparison Principle and Applications -- 3.1.6 The Dirichlet Problem and Perron's Method -- 3.1.7 Sections of Convex Functions -- 3.2 Geometry of Sections of Solutions to the Monge-Ampère Equation -- 3.2.1 Compactness of Solutions to the Monge-Ampère Equation -- 3.2.2 Caffarelli's Localization Theorem -- 3.2.3 Strict Convexity and C1,α Estimates -- 3.2.4 Engulfing Property of Sections -- Appendix A: Auxiliary Lemmas -- Appendix B: A Heuristic Explanation of Trudinger-Wang's Non-smooth Example -- References -- Part II Dynamical Properties of Hamilton-Jacobi Equations via the Nonlinear Adjoint Method: Large Time Behavior and Discounted Approximation -- Introduction -- Notations -- References -- 4 Ergodic Problems for Hamilton-Jacobi Equations -- 4.1 Motivation -- 4.2 Existence of Solutions to Ergodic Problems -- References -- 5 Large Time Asymptotics of Hamilton-Jacobi Equations -- 5.1 A Brief Introduction -- 5.2 First-Order Case with Separable Hamiltonians -- 5.2.1 First Example -- 5.2.2 Second Example -- 5.3 First-Order Case with General Hamiltonians -- 5.3.1 Formal Calculation -- 5.3.2 Regularizing Process -- 5.3.3 Conservation of Energy and a Key Observation -- 5.3.4 Proof of Key Estimates -- 5.4 Degenerate Viscous Case -- 5.5 Asymptotic Profile of the First-Order Case -- 5.6 Viscous Case -- 5.7 Some Other Directions and Open Questions -- References.
6 Selection Problems in the Discounted Approximation Procedure -- 6.1 Selection Problems -- 6.1.1 Examples on Nonuniqueness of Ergodic Problems -- 6.1.2 Discounted Approximation -- 6.2 Regularizing Process -- 6.2.1 Regularizing Process and Construction of M -- 6.2.2 Stochastic Mather Measures -- 6.2.3 Key Estimates -- 6.3 Proof of Theorem 6.5 -- 6.4 Proof of the Commutation Lemma -- 6.5 Applications -- 6.5.1 Limit of u in Example 6.1 -- 6.5.2 Limit of u in Examples 6.3, 6.4 -- 6.6 Some Other Directions and Open Questions -- 6.6.1 Discounted Approximation Procedure -- 6.6.2 Vanishing Viscosity Procedure -- 6.6.3 Selection of Mather Measures -- References -- 7 Appendix of Part II -- 7.1 Motivation and Examples -- 7.1.1 Front Propagation Problems -- 7.1.2 Optimal Control Problems -- 7.1.2.1 Inviscid Cases -- 7.1.2.2 Viscous Cases -- 7.2 Definitions -- 7.3 Consistency -- 7.4 Comparison Principle and Uniqueness -- 7.5 Stability -- 7.6 Lipschitz Estimates -- 7.7 The Perron Method -- References.
Record Nr. UNISA-996466643603316
Le Nam Q  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran
Autore Le Nam Q
Edizione [1st ed. 2017.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Descrizione fisica 1 online resource (VII, 228 p. 16 illus., 1 illus. in color.)
Disciplina 515.353
Collana Lecture Notes in Mathematics
Soggetto topico Partial differential equations
Calculus of variations
Differential geometry
Partial Differential Equations
Calculus of Variations and Optimal Control; Optimization
Differential Geometry
ISBN 3-319-54208-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Part I The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation and Related Linearized Monge-Ampère Equation -- Introduction -- Notation -- 1 The Affine Bernstein and Boundary Value Problems -- 1.1 The Affine Bernstein and Boundary Value Problems -- 1.1.1 Minimal Graph -- 1.1.2 Affine Maximal Graph -- 1.1.3 The Affine Bernstein Problem -- 1.1.4 Connection with the Constant Scalar Curvature Problem -- 1.1.5 The First Boundary Value Problem -- 1.1.6 The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation -- 1.1.7 Solvability of the Second Boundary Value Problem -- 1.2 Existence of Solution to the Second Boundary Value Problem -- 1.2.1 Existence of Solution via Degree Theory and A Priori Estimates -- 1.2.2 Several Boundary Regularity Results for Monge-Ampère and Linearized Monge-Ampère Equations -- 1.3 Proof of Global W4,p and C4,α Estimates -- 1.3.1 Test Functions -- 1.3.2 L1 Bound and Lower Bound on the Hessian Determinant -- 1.3.3 Gradient Bound -- 1.3.4 Legendre Transform and Upper Bound on Hessian Determinant -- References -- 2 The Linearized Monge-Ampère Equation -- 2.1 The Linearized Monge-Ampère Equation and Interior Regularity of Its Solution -- 2.1.1 The Linearized Monge-Ampère Equation -- 2.1.2 Linearized Monge-Ampère Equations in Contexts -- 2.1.3 Difficulties and Expected Regularity -- 2.1.4 Affine Invariance Property -- 2.1.5 Krylov-Safonov's Harnack Inequality -- 2.1.6 Harnack Inequality for the Linearized Monge-Ampère Equation -- 2.2 Interior Harnack and Hölder Estimates for Linearized Monge-Ampère -- 2.2.1 Proof of Caffarelli-Gutiérrez's Harnack Inequality -- 2.2.2 Proof of the Interior Hölder Estimates for the Inhomogeneous Linearized Monge-Ampère Equation -- 2.3 Global Hölder Estimates for the Linearized Monge-Ampère Equations.
2.3.1 Boundary Hölder Continuity for Solutions of Non-uniformly Elliptic Equations -- 2.3.2 Savin's Localization Theorem -- 2.3.3 Proof of Global Hölder Estimates for the Linearized Monge-Ampère Equation -- References -- 3 The Monge-Ampère Equation -- 3.1 Maximum Principles and Sections of the Monge-Ampère Equation -- 3.1.1 Basic Definitions -- 3.1.2 Examples and Properties of the Normal Mapping and the Monge-Ampère Measure -- 3.1.3 Maximum Principles -- 3.1.4 John's Lemma -- 3.1.5 Comparison Principle and Applications -- 3.1.6 The Dirichlet Problem and Perron's Method -- 3.1.7 Sections of Convex Functions -- 3.2 Geometry of Sections of Solutions to the Monge-Ampère Equation -- 3.2.1 Compactness of Solutions to the Monge-Ampère Equation -- 3.2.2 Caffarelli's Localization Theorem -- 3.2.3 Strict Convexity and C1,α Estimates -- 3.2.4 Engulfing Property of Sections -- Appendix A: Auxiliary Lemmas -- Appendix B: A Heuristic Explanation of Trudinger-Wang's Non-smooth Example -- References -- Part II Dynamical Properties of Hamilton-Jacobi Equations via the Nonlinear Adjoint Method: Large Time Behavior and Discounted Approximation -- Introduction -- Notations -- References -- 4 Ergodic Problems for Hamilton-Jacobi Equations -- 4.1 Motivation -- 4.2 Existence of Solutions to Ergodic Problems -- References -- 5 Large Time Asymptotics of Hamilton-Jacobi Equations -- 5.1 A Brief Introduction -- 5.2 First-Order Case with Separable Hamiltonians -- 5.2.1 First Example -- 5.2.2 Second Example -- 5.3 First-Order Case with General Hamiltonians -- 5.3.1 Formal Calculation -- 5.3.2 Regularizing Process -- 5.3.3 Conservation of Energy and a Key Observation -- 5.3.4 Proof of Key Estimates -- 5.4 Degenerate Viscous Case -- 5.5 Asymptotic Profile of the First-Order Case -- 5.6 Viscous Case -- 5.7 Some Other Directions and Open Questions -- References.
6 Selection Problems in the Discounted Approximation Procedure -- 6.1 Selection Problems -- 6.1.1 Examples on Nonuniqueness of Ergodic Problems -- 6.1.2 Discounted Approximation -- 6.2 Regularizing Process -- 6.2.1 Regularizing Process and Construction of M -- 6.2.2 Stochastic Mather Measures -- 6.2.3 Key Estimates -- 6.3 Proof of Theorem 6.5 -- 6.4 Proof of the Commutation Lemma -- 6.5 Applications -- 6.5.1 Limit of u in Example 6.1 -- 6.5.2 Limit of u in Examples 6.3, 6.4 -- 6.6 Some Other Directions and Open Questions -- 6.6.1 Discounted Approximation Procedure -- 6.6.2 Vanishing Viscosity Procedure -- 6.6.3 Selection of Mather Measures -- References -- 7 Appendix of Part II -- 7.1 Motivation and Examples -- 7.1.1 Front Propagation Problems -- 7.1.2 Optimal Control Problems -- 7.1.2.1 Inviscid Cases -- 7.1.2.2 Viscous Cases -- 7.2 Definitions -- 7.3 Consistency -- 7.4 Comparison Principle and Uniqueness -- 7.5 Stability -- 7.6 Lipschitz Estimates -- 7.7 The Perron Method -- References.
Record Nr. UNINA-9910257380003321
Le Nam Q  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Dynamical systems IV : symplectic geometry and its applications / V. I. Arnold, S. P. Novikov (eds.)
Dynamical systems IV : symplectic geometry and its applications / V. I. Arnold, S. P. Novikov (eds.)
Edizione [2nd, expanded and rev. ed.]
Pubbl/distr/stampa Berlin ; New York : Springer, c2001
Descrizione fisica 335 p. : ill. ; 24 cm
Disciplina 516.362
Altri autori (Persone) Arnold, Vladimir Igorevic
Novikov, Sergei Petrovichauthor
Collana Encyclopaedia of mathematical sciences, 0938-0396 ; 4
Soggetto topico Differential geometry
Symplectic manifolds
ISBN 3540626352
Classificazione AMS 00A20
AMS 58F05
AMS 58F06
AMS 58F07
AMS 70H
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991000837499707536
Berlin ; New York : Springer, c2001
Materiale a stampa
Lo trovi qui: Univ. del Salento
Opac: Controlla la disponibilità qui
Einfuhrung in die Differentialgeometrie / von Wilhelm Blaschke und Hans Reichardt
Einfuhrung in die Differentialgeometrie / von Wilhelm Blaschke und Hans Reichardt
Autore Blaschke, Wilhelm
Edizione [2te Aufl]
Pubbl/distr/stampa Berlin : Springer-Verlag, 1960
Descrizione fisica 173 p. ill. ; 24 cm.
Disciplina 516.36
Collana Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 0072-7830 ; 58
Soggetto topico Differential geometry
Classificazione AMS 53-XX
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione ger
Record Nr. UNISALENTO-991000843149707536
Blaschke, Wilhelm  
Berlin : Springer-Verlag, 1960
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt
Edizione [1st ed. 2000.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Descrizione fisica 1 online resource (XIII, 433 p.)
Disciplina 530.11
Collana Lecture Notes in Physics
Soggetto topico Differential geometry
Gravitation
Physics
Differential Geometry
Classical and Quantum Gravitation, Relativity Theory
Mathematical Methods in Physics
ISBN 3-540-46580-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics -- The Cauchy Problem for the Einstein Equations -- Post-Newtonian Gravitational Radiation -- Duality and Hidden Symmetries in Gravitational Theories -- Time-Independent Gravitational Fields -- Gravitational Lensing from a Geometric Viewpoint.
Record Nr. UNINA-9910139813603321
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt
Edizione [1st ed. 2000.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Descrizione fisica 1 online resource (XIII, 433 p.)
Disciplina 530.11
Collana Lecture Notes in Physics
Soggetto topico Differential geometry
Gravitation
Physics
Differential Geometry
Classical and Quantum Gravitation, Relativity Theory
Mathematical Methods in Physics
ISBN 3-540-46580-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics -- The Cauchy Problem for the Einstein Equations -- Post-Newtonian Gravitational Radiation -- Duality and Hidden Symmetries in Gravitational Theories -- Time-Independent Gravitational Fields -- Gravitational Lensing from a Geometric Viewpoint.
Record Nr. UNISA-996466685503316
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Elementare differentialgeometrie / W. Blaschke, K. Leichtweiss
Elementare differentialgeometrie / W. Blaschke, K. Leichtweiss
Autore Blaschke, Wilhelm
Edizione [5. voll. neubearb. aufl.]
Pubbl/distr/stampa Berlin : Springer-Verlag, 1973
Descrizione fisica x, 369 p. ; 24 cm.
Disciplina 516.36
Altri autori (Persone) Leichtweiss, K.
Collana Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 0072-7830 ; 1
Soggetto topico Differential geometry
Differential geometry-textbooks
ISBN 3540058893
Classificazione AMS 53-01
AMS 53-XX
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione ger
Record Nr. UNISALENTO-991000845709707536
Blaschke, Wilhelm  
Berlin : Springer-Verlag, 1973
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Elementary differential geometry / Barrett O'Neill
Elementary differential geometry / Barrett O'Neill
Autore O'Neill, Barrett
Pubbl/distr/stampa New York : Academic Press, c1966
Descrizione fisica viii, 409 p. ; 24 cm
Disciplina 516.3602
Soggetto topico Differential geometry
Classificazione AMS 53-01
AMS 53-XX
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991000846929707536
O'Neill, Barrett  
New York : Academic Press, c1966
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Elementary differential geometry / Andrew Pressley
Elementary differential geometry / Andrew Pressley
Autore Pressley, Andrew
Pubbl/distr/stampa London : Springer-Verlag, c2001
Descrizione fisica ix, 332 p. : ill. ; 24 cm
Disciplina 516.36
Collana Springer undergraduate mathematics series, 1615-2085
Soggetto topico Differential geometry
Mathematics and statistics-textbooks
ISBN 1852331526
Classificazione AMS 53-01
LC QA641.P68
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991003677089707536
Pressley, Andrew  
London : Springer-Verlag, c2001
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Elementary Symplectic Topology and Mechanics [[electronic resource] /] / by Franco Cardin
Elementary Symplectic Topology and Mechanics [[electronic resource] /] / by Franco Cardin
Autore Cardin Franco
Edizione [1st ed. 2015.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Descrizione fisica 1 online resource (237 p.)
Disciplina 510
515.64
516.36
530.15
Collana Lecture Notes of the Unione Matematica Italiana
Soggetto topico Mathematical physics
Differential geometry
Calculus of variations
Mathematical Physics
Differential Geometry
Calculus of Variations and Optimal Control; Optimization
ISBN 3-319-11026-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Beginning -- Notes on Differential Geometry -- Symplectic Manifolds -- Poisson brackets environment -- Cauchy Problem for H-J equations -- Calculus of Variations and Conjugate Points -- Asymptotic Theory of Oscillating Integrals -- Lusternik-Schnirelman and Morse -- Finite Exact Reductions -- Other instances -- Bibliography.
Record Nr. UNINA-9910299778503321
Cardin Franco  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
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