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Geometric methods in PDE’s / / edited by Giovanna Citti, Maria Manfredini, Daniele Morbidelli, Sergio Polidoro, Francesco Uguzzoni
| Geometric methods in PDE’s / / edited by Giovanna Citti, Maria Manfredini, Daniele Morbidelli, Sergio Polidoro, Francesco Uguzzoni |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (381 p.) |
| Disciplina | 515.353 |
| Collana | Springer INdAM Series |
| Soggetto topico |
Partial differential equations
Functional analysis Potential theory (Mathematics) Calculus of variations Fourier analysis Differential geometry Partial Differential Equations Functional Analysis Potential Theory Calculus of Variations and Optimal Control; Optimization Fourier Analysis Differential Geometry |
| ISBN | 3-319-02666-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 On Friedrichs commutators lemma for Hardy spaces and applications. Jorge Hounie -- 2 On the Hardy constant of some non-convex planar domains. Gerassimos Barbatis and Achilles Tertikas -- 3 Sharp singular Trudinger-Moser-Adams type inequalities with exact growth. Nguyen Lam and Guozhen Lu. 4 A Quantitative Lusin Theorem for Functions in BV. András Telcs and Vincenzo Vespri -- 5 X-Elliptic Harmonic Maps. Sorin Dragomir -- 6 Sum operators and Fefferman - Phong inequalities. Giuseppe Di Fazio, Maria Stella Fanciullo, Pietro Zamboni -- 7 Lp-parabolic regularity and non-degenerate Ornstein-Uhlenbeck type Operators. Enrico Priola -- 8 Local solvability of nonsmooth Hörmander’s operators. Marco Bramanti -- 9 Multiple solutions for an eigenvalue problem involving non–local elliptic p–Laplacian operators. Patrizia Pucci and Sara Saldi -- 10 Uniqueness of solutions of a class of quasilinear subelliptic equations. Lorenzo D’Ambrosio and Enzo Mitidieri -- 11 Liouville type theorems for non-linear differential inequalities on Carnot groups. Luca Brandolini and Marco Magliaro -- 12 Modica type gradient estimates for reaction-diffusion equations. Agnid Banerjee and Nicola Garofalo -- 13 A few recent results on fully nonlinear pde’s. Italo Capuzzo Dolcetta -- 14 Hölder regularity of the gradient for solutions of fully nonlinear equations with sub linear first order term. Isabeau Birindelli and Francoise Demengel -- 15 The Reflector Problem and the inverse square law. Cristian E. Gutiérrez and Ahmad Sabra -- 16 Gagliardo-Nirenberg inequalities for horizontal vector fields in the Engel group and in the 7-dimensional quaternionic Heisenberg group. Annalisa Baldi, Bruno Franchi and Francesca Tripaldi -- 17 Regularity of the free boundary in problems with distributed sources. Daniela De Silva, Fausto Ferrari, Sandro Salsa -- 18 The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE. Andrea Bonfiglioli, Giovanna Citti, Giovanni Cupini, Maria Manfredini, Annamaria Montanari, Daniele Morbidelli, Andrea Pascucci, Sergio Polidoro, Francesco Uguzzoni. |
| Record Nr. | UNINA-9910300251003321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Kolmogorov Operators and Their Applications
| Kolmogorov Operators and Their Applications |
| Autore | Menozzi Stéphane |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore Pte. Limited, , 2024 |
| Descrizione fisica | 1 online resource (354 pages) |
| Altri autori (Persone) |
PascucciAndrea
PolidoroSergio |
| Collana | Springer INdAM Series |
| ISBN | 981-9702-25-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Contents -- Local Regularity for the Landau Equation (with Coulomb Interaction Potential) -- 1 The Landau Equation and the Regularity Problem -- 2 Fundamental Properties of the Landau Collision Integral -- 2.1 Conservation Laws and H-Theorem -- 2.2 The Entropy Production and the Fisher Information -- 3 Weak Solutions -- 4 Local Regularity -- 5 Mathematical Tools -- 5.1 Ellipticity Bound -- 5.2 Locally Bounded Solutions Are Smooth -- 5.3 Truncated Entropy Inequality -- 5.4 Scalings -- 5.5 Local Regularity Criterion -- 6 A Sketch of the Proof of Theorem 4 -- 6.1 Local L2t,v Bound -- 6.2 Local L∞t,v Bound of the Diffusion Matrix -- 6.3 Deducing Local Regularity from Lemmas 6 and 7 -- 7 Conclusion and Final Remarks -- References -- L2 Hypocoercivity Methods for Kinetic Fokker-Planck Equations with Factorised Gibbs States -- 1 Introduction -- 2 From Microscopic and Macroscopic Coercivity to Hypocoercivity -- 3 Fokker-Planck Equations with Various External Potentials, Moments and Functional Inequalities -- 3.1 Strong Confinement Case: Poincaré Inequality -- 3.2 Weak Confinement Case: Weighted Poincaré Inequality -- 3.3 Weak Confinement, a Limit Case: Hardy-Poincaré Inequality -- 3.4 Very Weak Confinement Case: Caffarelli-Kohn-Nirenberg Inequality -- 3.5 No Potential Case: Nash's Inequality -- 3.6 A Short Summary -- 4 Kinetic Fokker-Planck Equations and Hypocoercivity Results -- 4.1 State of the Art -- 4.2 Notation and Basic Observations -- 4.3 Main Result -- 4.4 An Estimate of the Entropy Production -- 4.5 Moment Estimates -- 4.6 Proof of Theorem Main -- bullet Case alpha=1 and beta=1 -- bullet Case beta in (0,1) and alpha=1 -- bullet Case beta in (0,1) and alpha in (0,1) -- bullet Case beta in (0,1) and alpha in (0,1) -- bullet Case beta=1 and alpha=0 -- bullet Case beta in (0,1) and alpha=0 -- References.
New Perspectives on Recent Trends for Kolmogorov Operators -- 1 Introduction -- 1.1 Geometrical Setting -- 1.2 Fundamental Solution -- 1.3 Plan of the Paper -- 2 Functional Setting -- 2.1 Poincaré Inequality -- 2.2 Sobolev-Type Inequality -- 3 De Giorgi-Nash-Moser Weak Regularity Theory -- 3.1 Local Boundedness Estimates -- 3.2 Weak Harnack Inequality -- 3.3 Applications of the Harnack Inequality -- 4 Applications to Physics and Economics -- 4.1 American and Asian Options -- 4.2 Relativistic Fokker-Planck Equation -- 4.3 Boltzmann Equation -- 5 Nonlocal Kolmogorov-Fokker-Planck Equations -- 5.1 Geometric and Functional Setting -- 5.2 Boundedness Estimate -- 5.3 Further Developments -- References -- Schauder Estimates for Kolmogorov-Fokker-Planck Operators with Coefficients Measurable in Time and Hölder Continuous in Space -- 1 Introduction and Main Results -- 1.1 Structure of the Paper -- 2 Operators with Measurable Coefficients aij( t) -- 2.1 The Fundamental Solution of the Operator with Time Dependent Coefficients -- 2.2 Representation Formulas for u and ∂xixj2u in terms of Lu -- 2.3 Schauder Estimates in Space -- 2.4 Schauder Estimates in Space and Time -- 3 Schauder Estimates for Operators with Coefficients Depending on ( x,t) -- 3.1 Local Schauder Estimates in Space -- 3.2 Some Interpolation Inequalities -- 3.3 Global Schauder Estimates in Space -- References -- A New Proof of the Geometric Sobolev Embedding for Generalised Kolmogorov Operators -- 1 Introduction -- 2 Preliminaries -- 2.1 Fractional Powers of A, and Their Sobolev Embeddings -- 2.2 Nonlocal Perimeters and Coarea Formulas -- 3 Proofs -- References -- Intrinsic Taylor Formula for Non-homogeneous Kolmogorov-Type Lie Groups -- 1 Introduction -- 2 Intrinsic Hölder Spaces and Taylor Formula -- 3 Proof of Theorem 2.1 -- References -- Form-Boundedness and SDEs with Singular Drift. 1 Introduction -- 2 Notations -- 3 Form-Bounded Drifts. Semigroup in L2 -- 4 Sharp Solvability -- 4.1 Critical Magnitude of Drift Singularities -- 5 Three Approaches to Constructing Feller Semigroup for -+ b · -- 6 Basic Result on Weak Well-Posedness of SDEs with Singular Drift -- 7 Proof of Theorem 6.1 -- 8 Proof of Theorem 6.2 -- 9 Time-Inhomogeneous Form-Bounded Drifts and Feller Theory via Iterations -- 10 SDEs with Time-Inhomogeneous Form-Bounded Drifts -- 11 ``Form-Bounded'' Diffusion Coefficients -- 12 Stochastic Transport Equation and Strong Solutions to SDEs -- 13 Strong Well-Posedness via Röckner-Zhao's Approach -- 14 More Singular than Form-Bounded. Semigroup in W12,2 -- 15 Weakly Form-Bounded Drifts and SDEs -- 16 Time-Inhomogeneous Drifts in Morrey Class -- 17 SDEs Driven by α-Stable Process -- Appendix A: Proof of Lemma 6.1 -- Appendix B: Some Examples of Form-Bounded Vector Fields -- Appendix C: Smooth Approximations of Form-Bounded (-Type) Vector Fields -- Appendix D: Trotter's Approximation Theorem -- References -- About the Regularity of Degenerate Non-local Kolmogorov Operators Under Diffusive Perturbations -- 1 Introduction -- 1.1 General Aims and Scopes -- 1.2 The Model -- 2 Useful Notations -- 2.1 Definition of Solution -- 2.2 Definition of the Anisotropic Norms -- 3 Main Results -- 4 Proof of the Main Result -- References -- Integration by Parts Formula for Exit Times of One Dimensional Diffusions -- 1 Introduction -- 2 Preliminaries -- 2.1 Assumptions -- 2.2 A Reflection Principle -- 2.3 The Underlying Markov Chain and Associated Simplified Malliavin Calculus -- 3 The Probabilistic Representation for the First Hitting Time -- 3.1 Preliminaries -- 4 IBP Formulas with Respect to the Exit Time -- 4.1 IBP with Respect to Generalized Inverse Gaussian Times -- 4.2 Conditioning on the Space Variables -- 4.3 The Transfer Formula. 4.4 The IBP Formula -- Appendix -- The Malliavin Variance -- Auxiliary Lemmas for Lévy and Generalized Inverse Gaussian Distributions -- References -- On Averaged Control and Iteration Improvement for a Class of Multidimensional Ergodic Diffusions -- 1 Introduction -- 2 Assumptions and Auxiliaries -- 3 Main Results -- References. |
| Record Nr. | UNINA-9910865258903321 |
Menozzi Stéphane
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| Singapore : , : Springer Singapore Pte. Limited, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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