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April  2010, 26(2): 481-492. doi: 10.3934/dcds.2010.26.481

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, Italy, Italy

Received  October 2008 Revised  July 2009 Published  October 2009

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.
Keywords: degenerate parabolic equations, Doubly non-linear, local properties..
Mathematics Subject Classification: Primary: 35K65, 35B65; Secondary 35B4.
Citation: Simona Fornaro, Ugo Gianazza. Local properties of non-negative solutions to some doubly non-linear degenerate parabolic equations. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 481-492. doi: 10.3934/dcds.2010.26.481
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