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arXiv · 1610.09216

On viscosity and weak solutions for non-homogeneous p-Laplace equations

Maria Medina·Pablo Ochoa
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Abstract

In this manuscript we study the relation between viscosity and weak solutions for non-homogeneous p-Laplace equations with lower order term depending on $x$, $u$ and $\nabla u$. More precisely, we prove that any locally bounded viscosity solution constitutes a weak solution, extending previous results by Juutinen, Lindqvist and Manfredi on the homogeneous case, and Julin and Juutinen for a linear right hand side. Moreover, we provide a converse statement in the full case under extra assumptions on the regularity of the solutions.

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Maria Medina, Pablo Ochoa. 2016-10-28. On viscosity and weak solutions for non-homogeneous p-Laplace equations. https://arxiv.org/abs/1610.09216

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