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

By María Medina, Pablo Ochoa. 2016

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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 ∇ ⁡ u {\nabla u} . More precisely, we prove that any locally bounded viscosity solution constitutes a weak solution, extending results presented in Juutinen, Lindqvist and Manfredi [9], and Julin and Juutinen [6]. Moreover, we provide a converse statement in the full case under extra assumptions on the data.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c9e8a5f8bcb58bab09756d978328e0b49382e722