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arXiv · 2407.20011

An implicit two-phase obstacle-type problem for the $p$-Laplacian with the fractional gradient

Pedro Miguel Campos·José Francisco Rodrigues
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Abstract

In this work we study an inhomogeneous two-phase obstacle-type problem associated to the $s$-fractional $p$-Laplacian. Besides the existence and uniqueness of solutions, we study the convergence of the solutions when $s\to 1$ to the classical problem. We also study the continuous dependence with respect to the level-set function $v$, yielding an existence result for a two-phase obstacle-type problem with an implicit level-set function.

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Pedro Miguel Campos, José Francisco Rodrigues. 2024-07-29. An implicit two-phase obstacle-type problem for the $p$-Laplacian with the fractional gradient. https://arxiv.org/abs/2407.20011

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