Calculus of Variations and Geometric Measure Theory
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M. Masson - M. J. Miranda - F. Paronetto - M. Parviainen

Local higher integrability for parabolic quasiminimizers in metric spaces

created by miranda on 15 May 2014


Published Paper

Inserted: 15 may 2014
Last Updated: 15 may 2014

Journal: Ricerche di Matematica
Volume: 62
Number: 2
Pages: 279-305
Year: 2013
Doi: 10.1007/s11587-013-0150-z


Usingpurelyvariationalmethods,weproveinmetricmeasurespaceslocal 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.


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