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arXiv · 1810.11616

A picone Identity for variable exponent operators and applications

Rakesh Arora·Jacques Giacomoni·Guillaume Warnault
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Abstract

In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the $p(x)$-Laplacian defined as $\mbox{div}(|\nabla u|^{p(x)-2} \nabla u).$ Our extension provides a new version of the Diaz-Saa inequality and new uniqueness results to some quasilinear elliptic equations with variable exponents. This new Picone identity can be also used to prove some accretivity property to a class of fast diffusion equations involving variable exponents. Using this, we prove for this class of parabolic equations a new weak comparison principle.

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Rakesh Arora, Jacques Giacomoni, Guillaume Warnault. 2018-10-27. A picone Identity for variable exponent operators and applications. https://arxiv.org/abs/1810.11616

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