Equivalence of viscosity and weak solutions for the normalized <Emphasis Type="Italic">p</Emphasis>(<Emphasis Type="Italic">x</Emphasis>)-Laplacian |
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Authors: | Email author" target="_blank">Jarkko?SiltakoskiEmail author |
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Institution: | 1.Department of Mathematics and Statistics,University of Jyv?skyl?,Jyv?skyl?,Finland |
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Abstract: | We show that viscosity solutions to the normalized p(x)-Laplace equation coincide with distributional weak solutions to the strong p(x)-Laplace equation when p is Lipschitz and \(\inf p>1\). This yields \(\smash {C^{1,\alpha }}\) regularity for the viscosity solutions of the normalized p(x)-Laplace equation. As an additional application, we prove a Radó-type removability theorem. |
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