user's guide to viscosity solutions\\ of second order\\ partial differential equations
نویسندگان
چکیده
منابع مشابه
User’s Guide to Viscosity Solutions of Second Order Partial Differential Equations
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-cont...
متن کاملViscosity Solutions to Second Order Partial Differential Equations on Riemannian Manifolds, I
We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations F (x, u(x), du(x), du(x)) = 0 defined on a finite-dimensional Riemannian manifold M . Finest results (with hypothesis that require the function F to be degenerate elliptic, that is nonincreasing in the second order derivative variable) are ...
متن کاملViscosity Solutions to Second Order Partial Differential Equations on Riemannian Manifolds
We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations F (x, u, du, du) = 0 defined on a finite-dimensional Riemannian manifold M . Finest results (with hypothesis that require the function F to be degenerate elliptic, that is nonincreasing in the second order derivative variable, and uniformly...
متن کاملSecond-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
The aim of this work is to revisit viscosity solutions’ theory for second-order elliptic integrodifferential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main contribution is a new Jensen-Ishii’s Lemma for integro-differential equations, which is stated for solutions with no restriction on their growth at infinity. The pr...
متن کاملThe Maximum Principle for Viscosity Solutions of Fully Nonlinear Second Order Partial Differential Equations
We prove that viscosity solutions in W 1'~176 of the second order, fully nonlinear, equation F(D2u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) Fis uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions ont...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1992
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1992-00266-5