A New Proof for the Equivalence of Weak and Viscosity Solutions for the p-Laplace Equation
By Vesa Julin, Petri Juutinen. 2011
96 citations recorded by the source corpus.
In this paper, we give a new proof for the fact that the distributional weak solutions and the viscosity solutions of the p-Laplace equation −div(|Du| p−2 Du) = 0 coincide. Our proof is more direct and transparent than the original proof of Juutinen et al. [8], which relied on the full uniqueness machinery of the theory of viscosity solutions. We establish a similar result also for the solutions of the non-homogeneous version of the p-Laplace equation.
Subfields: Applied Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/cd277b210572fe2fd0f152e64cc02e428076bb97
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In Applied Mathematics
- Hannes Luiro
- Pablo Ochoa
- María Medina
- Mikko Parviainen
- Eero Saksman
- Emanuel Carneiro
- Verena Bogelein
- Ondvrej Kurka
In Control and Systems Engineering
Citations in the corpus
- On viscosity and weak solutions for non-homogeneous p-Laplace equations (2016, methodology): “In [9], Juutinen, Lindqvist and Manfredi showed that the notion of p-harmonic solution is equivalent to the notion of viscosity solution.”
- Harnack's Inequality for p-Harmonic Functions via Stochastic Games (2012, background): “Moreover, viscosity solutions to p-Laplacian coincide with the classical ones by [9] (see [8] for easier proof of this fact).”
- Equivalence of solutions to fractional p-Laplace type equations (2016, unknown): “nverge to the ones of p-Laplacian as s→ 1. In the case of the p-Laplace equation, the equivalence of solutions was first proved in [JLM01] (see also [Lin86]), and a shorter proof was recently given in [JJ12]. It is notable that both in [JLM01] and in [JJ12] there is a need for a technical regularizat”