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On the solutions of nonlocal 1-Laplacian equation with $L^1$-data | | Dingding Li
; Chao Zhang
; | | Date: |
1 Nov 2023 | | Abstract: | We study the solutions to a nonlocal 1-Laplacian equation given by $$ 2 ext{P.V.}int_{mathbb{R}^N}frac{u(x)-u(y)}{|u(x)-u(y)|} frac{dy}{|x-y|^{N+s}}=f(x) quad extmd{for } xin Omega, $$ with Dirichlet boundary condition $u(x)=0$ in $mathbb R^Nackslash Omega$ and nonnegative $L^1$-data. By investigating the asymptotic behaviour of renormalized solutions $u_p$ to the nonlocal $p$-Laplacian equations as $p$ goes to $1^+$, we introduce a suitable definition of solutions and prove that the limit function $u$ of ${u_p}$ is a solution of the nonlocal $1$-Laplacian equation above. | | Source: | arXiv, 2311.00218 | | Services: | Forum | Review | PDF | Favorites | |
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