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

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...

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Bibliographic Details
Published inAdvances in continuous and discrete models Vol. 2023; no. 1; p. 8
Main Author Bungert, Leon
Format Journal Article
LanguageEnglish
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
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Summary: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 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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1687-1839
2731-4235
1687-1847
DOI:10.1186/s13662-023-03754-8