LEADER 04294nam 22006255 450 001 9910299787703321 005 20200702052346.0 010 $a3-319-12829-9 024 7 $a10.1007/978-3-319-12829-0 035 $a(CKB)3710000000306160 035 $a(EBL)1967017 035 $a(SSID)ssj0001386561 035 $a(PQKBManifestationID)11755226 035 $a(PQKBTitleCode)TC0001386561 035 $a(PQKBWorkID)11374353 035 $a(PQKB)10427939 035 $a(DE-He213)978-3-319-12829-0 035 $a(MiAaPQ)EBC1967017 035 $a(PPN)183091361 035 $a(EXLCZ)993710000000306160 100 $a20141126d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L? /$fby Nikos Katzourakis 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (125 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 $a3-319-12828-0 320 $aIncludes bibliographical references. 327 $aPreface; Acknowledgments; Contents; 1 History, Examples, Motivation and First Definitions; References; 2 Second Definitions and Basic Analytic Properties of the Notions; References; 3 Stability Properties of the Notions and Existence via Approximation; References; 4 Mollification of Viscosity Solutions and Semiconvexity; References; 5 Existence of Solution to the Dirichlet Problem via Perron's Method; References; 6 Comparison Results and Uniqueness of Solution to the Dirichlet Problem; References 327 $a7 Minimisers of Convex Functionals and Existence of Viscosity Solutions to the Euler-Lagrange PDEReferences; 8 Existence of Viscosity Solutions to the Dirichlet Problem for the infty-Laplacian; References; 9 Miscellaneous Topics and Some Extensions of the Theory; 9.1 Fundamental Solutions of the infty-Laplacian; 9.1.1 The infty-Laplacian and Tug-of-War Differential Games; 9.1.2 Discontinuous Coefficients, Discontinuous Solutions; 9.1.3 Barles-Perthame Relaxed Limits (1-Sided Uniform Convergence) and Generalised 1-Sided Stability; 9.1.4 Boundary Jets and Jets Relative to Non-open Sets 327 $a9.1.5 Nonlinear Boundary Conditions9.1.6 Comparison Principle for Viscosity Solutions Without Decoupling in the x-variable; References 330 $aThe purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aPartial differential equations 606 $aCalculus of variations 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 615 0$aPartial differential equations. 615 0$aCalculus of variations. 615 14$aPartial Differential Equations. 615 24$aCalculus of Variations and Optimal Control; Optimization. 676 $a510 676 $a515.353 676 $a515.64 700 $aKatzourakis$b Nikos$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768293 906 $aBOOK 912 $a9910299787703321 996 $aIntroduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L?$91564836 997 $aUNINA