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- W4287322409 abstract "We prove the (optimal) $W^{1,infty}$-regularity of weak solutions to the equation $-Delta u = Q ; mathcal{H}^{n-1} llcorner Gamma$ in a domain $Omega subset mathbb{R}^n$ with Dirichlet boundary conditions, where $Gamma subset subset Omega$ is a compact (Lipschitz) manifold and $Q in L^infty(Gamma)$. We also discuss optimality and necessity of the assumptions on $Q$ and $Gamma$. Our findings can be applied to study the regularity of solutions for several free boundary problems, in particular the biharmonic Alt-Caffarelli Problem." @default.
- W4287322409 created "2022-07-25" @default.
- W4287322409 creator A5051084007 @default.
- W4287322409 date "2021-02-27" @default.
- W4287322409 modified "2023-09-30" @default.
- W4287322409 title "The Poisson equation involving surface measures" @default.
- W4287322409 doi "https://doi.org/10.48550/arxiv.2103.00303" @default.
- W4287322409 hasPublicationYear "2021" @default.
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