Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
نویسندگان
چکیده
منابع مشابه
Second-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 کاملLarge Time Behavior of Periodic Viscosity Solutions for Uniformly Elliptic Integro-differential Equations
In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem (or cell problem), i.e. we construct solutions of the form λt+v(x). We then prove that solutions of the Cauchy problem look like those specific solutions as time goes to infinity. We face ...
متن کاملTopics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations
The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of their consequences. 2000 Mathematics Subject Classification. Primary 35J15; Secondary 35B05, 35C15, 35K10.
متن کاملOn the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations
In this article, we consider the analogue of the Dirichlet problem for second-order elliptic integro-differential equations, which consists in imposing the “boundary conditions” in the whole complementary of the domain. We are looking for conditions on the differential and integral parts of the equation in order to ensure that the Dirichlet boundary condition is satisfied in the classical sense...
متن کاملStability properties of second order delay integro-differential equations
A basic theorem on the behavior of solutions of scalar linear second order delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.
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: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2008
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2007.02.007