Abstract
We study two obstacle problems involving the p-Laplace operator in domains with n-th pre-fractal and fractal boundary. We perform asymptotic analysis for \begin{document} $p \to \infty $ \end{document} and \begin{document} $n \to \infty $ \end{document} .
Highlights
In this paper we consider obstacle problems involving p-Laplacian in bad domains in R2
We study two obstacle problems involving the p-Laplace operator in domains with n-th pre-fractal and fractal boundary
With “bad domains” we refer to domains with pre-fractal and fractal boundary
Summary
In this paper we consider obstacle problems involving p-Laplacian in bad domains in R2. In [13] the authors study a double obstacle problem for p-Laplacian in smooth domains and by passing to the limit as p → ∞ they obtain a complete answer to an optimal mass transport problem for the Euclidean distance. We recall that this connection was the key to the first complete proof of the existence of an optimal transport map for the classical Monge problem (see [9]). Given f ∈ L1(Ωα), we consider two obstacle problems involving p-Laplacian (p > 2) on domains with pre-fractal boundary Ωnα : find u ∈ Kn,
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