The inhomogeneous $p$-Laplacian equation with Neumann boundary conditions in the limit $p\to\infty$
| Autor: | Bungert, Leon |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Adv Cont Discr Mod 2023, 8 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1186/s13662-023-03754-8 |
| Popis: | We investigate the limiting behavior of solutions to the inhomogeneous $p$-Laplacian equation $-\Delta_p u = \mu_p$ 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. Comment: Corrected some typos |
| Databáze: | arXiv |
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