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- W4302017698 abstract "The question of unique continuation of harmonic functions in a domain $Omega$ $subset$ R d with boundary $partial$$Omega$, satisfying Dirichlet boundary conditions and with normal derivatives vanishing on a subset $omega$ of the boundary is a classical problem. When $omega$ contains an open subset of the boundary it is a consequence of Carleman estimates (uniqueness for second order elliptic operators across an hypersurface). The case where $omega$ is a set of positive (d -- 1) dimensional measure has attracted a lot of attention, see e.g. [10, 3, 15], where qualitative results have been obtained in various situations. The main open questions (about uniqueness) concern now Lipschitz domains and variable coefficients. Here, using results by Logunov and Malinnikova [13, 14], we consider the simpler case of W 2,$infty$ domains but prove quantitative uniqueness both for Dirichlet and Neumann boundary conditions. As an application, we deduce quantitative estimates for the Dirichlet and Neumann Laplace eigenfunctions on a W 2,$infty$ domain with boundary." @default.
- W4302017698 created "2022-10-06" @default.
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- W4302017698 date "2021-10-27" @default.
- W4302017698 modified "2023-10-10" @default.
- W4302017698 title "A remark on quantitative unique continuation from subsets of the boundary of positive measure" @default.
- W4302017698 doi "https://doi.org/10.48550/arxiv.2110.14282" @default.
- W4302017698 hasPublicationYear "2021" @default.
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