Global higher integrability for parabolic quasiminimizers in metric measure spaces

Mathias Masson; Mikko Parviainen

doi:10.1007/s11854-015-0019-z

Global higher integrability for parabolic quasiminimizers in metric measure spaces

Mathias Masson^*, Mikko Parviainen

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

University of Jyväskylä

Research output: Contribution to journal › Article › Scientific › peer-review

9 Citations (Scopus)

Abstract

We prove higher integrability up to the boundary for minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces related to the heat equation. We assume the underlying metric measure space to be equipped with a doubling measure and to support a weak Poincaré inequality. The boundary of the domain is assumed to satisfy a regularity condition.

Original language	English
Pages (from-to)	307-339
Number of pages	33
Journal	JOURNAL D ANALYSE MATHEMATIQUE
Volume	126
Issue number	1
DOIs	https://doi.org/10.1007/s11854-015-0019-z
Publication status	Published - 20 Apr 2015
MoE publication type	A1 Journal article-refereed

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10.1007/s11854-015-0019-z

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abstract = "We prove higher integrability up to the boundary for minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces related to the heat equation. We assume the underlying metric measure space to be equipped with a doubling measure and to support a weak Poincar{\'e} inequality. The boundary of the domain is assumed to satisfy a regularity condition.",

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Global higher integrability for parabolic quasiminimizers in metric measure spaces

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