Equivalence of viscosity and weak solutions for the normalized p(x)-Laplacian
Siltakoski, J. (2018). Equivalence of viscosity and weak solutions for the normalized p(x)-Laplacian. Calculus of Variations and Partial Differential Equations, 57(4), Article 95. https://doi.org/10.1007/s00526-018-1375-1
© Springer-Verlag GmbH Germany, part of Springer Nature 2018.
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 C 1,α 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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