Local higher integrability for parabolic quasiminimizers in metric spaces

被引：16

作者：

Masson M. ^{[1
]}

Miranda Jr. M. ^{[2
]}

Paronetto F. ^{[3
]}

Parviainen M. ^{[4
]}

机构：

[1] Department of Mathematics and Systems Analysis, Aalto University School of Science, 00076 Helsinki

[2] Department of Mathematics and Computer Science, University of Ferrara, 44121 Ferrara

[3] Department of Mathematics, University of Padova, 35121 Padova

[4] Department of Mathematics and Statistics, University of Jyväskylä, 40014 Jyväskylä

来源：

Ricerche di Matematica | 2013年 / 62卷 / 2期

关键词：

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

D O I：

10.1007/s11587-013-0150-z

中图分类号：

学科分类号：

摘要：

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. © 2013 Università degli Studi di Napoli Federico II"."

引用

页码：279 / 305

页数：26

共 36 条

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