Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A Revisit-Reference-Cited by-同舟云学术

Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A Revisit

Published:2017-08-18 Issue:7 Volume:2019 Page:2085-2136
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Dong Hongjie¹,Kim Seick²

Affiliation:

1. Division of Applied Mathematics, Brown University, Providence, RI, USA

2. Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, Republic of Korea

Abstract

AbstractUnder various conditions, we establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving Hölder semi-norms not with respect to all, but only with respect to some of the independent variables. A novelty of our results is that the coefficients are allowed to be merely measurable with respect to the other independent variables.

Funder

National Science Foundation

Neurosciences Research Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2019/7/2085/28332941/rnx180.pdf

Reference28 articles.

1. “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I.”;Agmon;Comm. Pure Appl. Math.,1959

2. Fully Nonlinear Elliptic Equations