Summability of semicontinuous super solutions to a quasilinear parabolic equation

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Annali della Scuola Normale Superiore di Pisa- Classe di Scienze 4 (1):59-78 (2005)
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Abstract

We study the so-called $p$-superparabolic functions, which are defined as lower semicontinuous supersolutions of a quasilinear parabolic equation. In the linear case, when $p = 2$, we have supercaloric functions and the heat equation. We show that the $p$-superparabolic functions have a spatial Sobolev gradient and a sharp summability exponent is given

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10.2422/2036-2145.2005.1.03

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