Higher integrability for weak solutions to parabolic multi-phase equations

Bogi Kim, Jehan Oh

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we establish a local higher integrability result for the gradient of a weak solution to a parabolic multi-phase equation. To achieve this, we prove parabolic Poincaré type inequalities and reverse Hölder type inequalities for the gradient of a weak solution in each of difference types of intrinsic cylinders. In particular, we formulate a delicate plan of alternatives and stopping time arguments to address the presence of two different transitions.

Original languageEnglish
Pages (from-to)223-298
Number of pages76
JournalJournal of Differential Equations
Volume409
DOIs
StatePublished - 15 Nov 2024

Keywords

  • Degenerate parabolic equations
  • Higher integrability
  • Intrinsic cylinders
  • Multi-phase problems
  • Weak solution

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