Time Fractional Parabolic Equations with Measurable Coefficients and Embeddings for Fractional Parabolic Sobolev Spaces

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticlepeer-review

Abstract

We consider time fractional parabolic equations in divergence and non-divergence form when the leading coefficients aij are measurable functions of (t,x1) except for a11, which is a measurable function of either t or x1. We obtain the solvability in Sobolev spaces of the equations in the whole space, on a half space, and on a partially bounded domain. The proofs use a level set argument, a scaling argument, and embeddings in fractional parabolic Sobolev spaces for which we give a direct and elementary proof.

Original languageEnglish
Pages (from-to)17563-17610
Number of pages48
JournalInternational Mathematics Research Notices
Volume2021
Issue number22
DOIs
Publication statusPublished - 2021 Nov 1

ASJC Scopus subject areas

  • Mathematics(all)

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