Further Time Regularity for Nonlocal, Fully Nonlinear Parabolic Equations
نویسندگان
چکیده
منابع مشابه
A Counterexample to C Regularity for Parabolic Fully Nonlinear Equations
We address the self-similar solvability of a singular parabolic problem and show that solutions to parabolic fully nonlinear equations are not expected to be C.
متن کاملOn the Regularity Theory of Fully Nonlinear Parabolic Equations
Recently M. Crandall and P. L. Lions [3] developed a very successful method for proving the existence of solutions of nonlinear second-order partial differential equations. Their method, called the theory of viscosity solutions, also applies to fully nonlinear equations (in which even the second order derivatives can enter in nonlinear fashion). Solutions produced by the viscosity method are gu...
متن کاملPerron’s method for nonlocal fully nonlinear equations
This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perron’s method. If the equation is uniformly elliptic, we prove the discontinuous viscosity solution is Hölder continuous and thus it is a viscosity solution.
متن کاملQuadratic expansions and partial regularity for fully nonlinear uniformly parabolic equations
For a parabolic equation associated to a uniformly elliptic operator, we obtain a W 3,ε estimate, which provides a lower bound on the Lebesgue measure of the set on which a viscosity solution has a quadratic expansion. The argument combines parabolic W 2,ε estimates with a comparison principle argument. As an application, we show, assuming the operator is C1, that a viscosity solution is C2,α o...
متن کاملIntroduction to fully nonlinear parabolic equations
These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations. MSC. 35K55, 35D40, ...
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: Communications on Pure and Applied Mathematics
سال: 2016
ISSN: 0010-3640
DOI: 10.1002/cpa.21671