Harnack's inequality and the strong p ( ⋅ ) -Laplacian

We study solutions of the strong p ( ⋅ ) -Laplace equation. We show that, in contrast to p ( ⋅ ) -Laplace solutions, these solutions satisfy the ordinary, scale-invariant Harnack inequality. As consequences we derive the strong maximum principle and global integrability of solutions.

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Bibliographic Details
Published in:Journal of Differential Equations 2011-02, Vol.250 (3), p.1631-1649
Main Authors: Adamowicz, Tomasz, Hästö, Peter
Format: Article
Language:English
Subjects:
Caccioppoli estimate
Dirichlet energy
Harnack inequality
Non-standard growth
p-Laplace equation
Supersolution
Variable exponent
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Summary:We study solutions of the strong p ( ⋅ ) -Laplace equation. We show that, in contrast to p ( ⋅ ) -Laplace solutions, these solutions satisfy the ordinary, scale-invariant Harnack inequality. As consequences we derive the strong maximum principle and global integrability of solutions.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2010.10.006