Local properties of non-negative solutions to some doubly non-linear       degenerate parabolic equations

Simona Fornaro; Ugo Gianazza

doi:10.3934/dcds.2010.26.481

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2010, Volume 26, Issue 2: 481-492. Doi: 10.3934/dcds.2010.26.481

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Local properties of non-negative solutions to some doubly non-linear degenerate parabolic equations

Simona Fornaro^1, and
Ugo Gianazza^1,

1.
Dipartimento di Matematica "F. Casorati”, Università di Pavia, Via Ferrata 1, 27100 Pavia

Received: September 30, 2008

Revised: June 30, 2009

Published: June 2010

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Abstract

In the present paper we study the local behavior of non-negative weak solutions of a wide class of doubly non linear degenerate parabolic equations. We show, in particular, some lower pointwise estimates of such solutions in terms of suitable sub-potentials (dictated by the structure of the equation) and an alternative form of the Harnack inequality.

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Mathematics Subject Classification: Primary: 35K65, 35B65; Secondary 35B45.

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