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arXiv · 1201.5199

Discontinuous gradient constraints and the infinity Laplacian

Petri Juutinen·Mikko Parviainen·Julio D. Rossi
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Abstract

Motivated by tug-of-war games and asymptotic analysis of certain variational problems, we consider a gradient constraint problem involving the infinity Laplace operator. We prove that this problem always has a solution that is unique if a certain regularity condition on the constraint is satisfied. If this regularity condition fails, then solutions obtained from game theory and $L^p$-approximation need not coincide.

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Petri Juutinen, Mikko Parviainen, Julio D. Rossi. 2012-01-25. Discontinuous gradient constraints and the infinity Laplacian. https://arxiv.org/abs/1201.5199

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