Abstract
AbstractWe investigate the limiting behavior of solutions to the inhomogeneousp-Laplacian equation$-\Delta _{p} u = \mu _{p}$−Δpu=μpsubject to Neumann boundary conditions. For right-hand sides, which are arbitrary signed measures, we show that solutions converge to a Kantorovich potential associated with the geodesic Wasserstein-1 distance. In the regular case with continuous right-hand sides, we characterize the limit as viscosity solution to an infinity Laplacian / eikonal type equation.
Funder
Deutsche Forschungsgemeinschaft
Vetenskapsrådet
Rheinische Friedrich-Wilhelms-Universität Bonn
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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