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

Hongjie Dong, Seick Kim

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Under 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.

Original languageEnglish
Pages (from-to)2085-2136
Number of pages52
JournalInternational Mathematics Research Notices
Volume2019
Issue number7
DOIs
Publication statusPublished - 2019 Apr

Bibliographical note

Funding Information:
This work was partially supported by the NSF under agreements [DMS-1056737 and DMS-1600593

Publisher Copyright:
© 2017 The Author(s) 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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