Abstract:We propose an energy-based nonlocal $p$-Laplacian interface problem. Neumann interface conditions are naturally formulated via the energy, while Dirichlet conditions are enforced through a penalty term. A key feature is that the model retains a sharp interface, which facilitates extension to other interface problems; we illustrate this by developing a nonlocal approximation for the $p$-Laplacian interface problem with membrane conditions. By establishing $\Gamma$-convergence and compactness, we prove that as the nonlocal horizon vanishes, minimizers of the nonlocal functionals converge to those of the local counterparts. Numerical experiments using an efficient finite element method confirm the convergence.
From: Tangjun Wang [view email]
[v1]
Sat, 30 May 2026 07:52:11 UTC (425 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。