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Title of Journal: J Math Sci

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Abbravation: Journal of Mathematical Sciences

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Springer US

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1573-8795

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The Behavior of Solutions to the Dirichlet Problem

Authors: Yu Alkhutov M V Borsuk
Publish Date: 2015/09/21
Volume: 210, Issue: 4, Pages: 341-370
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Abstract

We study the Dirichlet problem for the pLaplacian in a conical domain with the homogeneous boundary condition on the lateral surface of a cone with vertex at the origin We assume that the variable exponent p = px is separated from 1 and ∞ and denote by Ω the intersection of the cone with the unit n − 1dimensional sphere We prove that i if p satisfies the Lipschitz condition and ∂Ω is of class C 2+β then the solution to the Dirichlet problem is Ox λ in a neighborhood of the origin where λ is the sharp exponent of tending to zero of solutions to the same Dirichlet problem for the p0Laplacian and ii if p satisfies the Hölder condition p0 = 2 and ∂Ω is of class C 1+β then the solution to the Dirichlet problem is Ox λ0 in a neighborhood of the origin where λ 0 is the sharp exponent of tending to zero of solutions to the same Dirichlet problem for the Laplace operator Bibliography 18 titles

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