Parabolic equations with unbounded lower-order coefficients in Sobolev spaces with mixed norms

Doyoon Kim, Seungjin Ryu, Kwan Woo

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the Lp,q-solvability of parabolic equations in divergence form with full lower-order terms. The coefficients and non-homogeneous terms belong to mixed Lebesgue spaces with the lowest integrability conditions. In particular, the coefficients for the lower-order terms are not necessarily bounded. We study both the Dirichlet and conormal derivative boundary value problems on irregular domains. We also prove embedding results for parabolic Sobolev spaces, the proof of which is of independent interest.

Original languageEnglish
Article number9
JournalJournal of Evolution Equations
Volume22
Issue number1
DOIs
Publication statusPublished - 2022 Mar

Keywords

  • Embedding theorem
  • Parabolic equations
  • Reifenberg flat domains
  • Sobolev spaces
  • Unbounded lower-order coefficients

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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