The inhomogeneous p-Laplacian equation with Neumann boundary conditions in the limit p

• Published in: Advances in continuous and discrete models Vol. 2023; no. 1; p. 8
• Main Author: Bungert, Leon
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2023; Springer Nature B.V
• Subjects: Analysis; Approximation; Boundary conditions; Difference and Functional Equations; Functional Analysis; Investigations; Laplace equation; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Viscosity; Viscosity solution; 35D30; Wasserstein distance; 35D40; Infinity Laplacian; 49Q22; Optimal transport; Laplacian

We investigate the limiting behavior of solutions to the inhomogeneous p -Laplacian equation − Δ p u = μ p subject 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 Wasser...