Harnack's inequality for the $p(x)$-Laplacian with a two-phase exponent $p(x)$

Yu. A. Alkhutov   ; M. D. Surnachev

Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 8-56

Résumé

One considers solutions of the $p(x)$-Laplacian equation in a neighborhood of a point $x_0$ on a hyperplane $\Sigma$. It is assumed that the exponent $p(x)$ possesses a logarithmic continuity modulus as $x_0$ is approached from one of the half-spaces separated by $\Sigma$. A version of the Harnack inequality is proved for these solutions.

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