Local higher integrability for parabolic quasiminimizers in metric spaces

Mathias Masson*, Michele Miranda, Fabio Paronetto, Mikko Parviainen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)

Abstract

Using purely variational methods, we prove in metric measure spaces local higher integrability for minimal p-weak upper gradients of parabolic quasiminimizers related to the heat equation. We assume the measure to be doubling and the underlying space to be such that a weak Poincaré inequality is supported. We define parabolic quasiminimizers in the general metric measure space context, and prove an energy type estimate. Using the energy estimate and properties of the underlying metric measure space, we prove a reverse Hölder inequality type estimate for minimal p-weak upper gradients of parabolic quasiminimizers. Local higher integrability is then established based on the reverse Hölder inequality, by using a modification of Gehring's lemma.

Original languageEnglish
Pages (from-to)279-305
Number of pages27
JournalRicerche di Matematica
Volume62
Issue number2
DOIs
Publication statusPublished - Nov 2013
MoE publication typeA1 Journal article-refereed

Keywords

  • Analysis on metric spaces
  • Calculus of variations
  • Energy estimates
  • Higher integrability
  • Newtonian spaces
  • Nonlinear parabolic equations
  • Parabolic quasiminima
  • Reverse Hölder inequality
  • Upper gradient

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