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- W4300986578 abstract "We study the regularity of Radon measures $mu$ which satisfy that there exists a function $h_mu$ in $H^1(Omega)$, stationary harmonic such that $Delta h_mu =mu$ in $Omega$ (here $Omega$ is an open set of $mathbb{R}^2$). Such conditions appear in physical contexts such as the study of a limiting vorticity measure associated to a family $(u_varepsilon)_varepsilon$ of solutions of the Ginzburg-Landau system without magnetic field. Under these conditions we prove that locally there exists a harmonic function $H$ such that the support of the measure is contained in the set of zeros of $H$. Using the local structure of the set of zeros of harmonic functions we can thus obtain that locally the support of $mu$ is a union of smooth simple" @default.
- W4300986578 created "2022-10-04" @default.
- W4300986578 creator A5081875325 @default.
- W4300986578 date "2015-04-28" @default.
- W4300986578 modified "2023-10-14" @default.
- W4300986578 title "Regularity properties of stationary harmonic functions whose Laplacian is a Radon measure" @default.
- W4300986578 doi "https://doi.org/10.48550/arxiv.1504.07457" @default.
- W4300986578 hasPublicationYear "2015" @default.
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