Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients
Year: 2020
Author: Hongjie Dong
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 2 : pp. 161–199
Abstract
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$ estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0021
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 2 : pp. 161–199
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 39
Keywords: Elliptic and parabolic equations and systems nonlocal equations fully nonlinear equations VMO and partially VMO coefficients weighted estimates Muckenhoupt weights.
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