Uniqueness results for inverse Robin problems with bounded coefficient

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• 作者：Laurent Baratchart^a ; ^{laurent.baratchart@inria.fr" class="auth_mail" title="E-mail the corresponding author} ; Laurent Bourgeois^b ; ^{laurent.bourgeois@ensta.fr" class="auth_mail" title="E-mail the corresponding author} ; Juliette Leblond^a ; ^{juliette.leblond@inria.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Robin inverse problem ; Holomorphic Hardy&ndash ; Smirnov classes ; Elliptic regularity ; Unique continuation
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：270
• 期：7
• 页码：2508-2542
• 全文大小：710 K

文摘

In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain Ω⊂Rⁿ$\mathrm{\Omega }\subset {\mathbb{R}}^n$, with L^∞$L^{\infty }$ Robin coefficient, L²$L^2$ Neumann data and conductivity of class W^1,r(Ω)$W^{1,r}(\mathrm{\Omega })$, r>n$r>n$. We show that uniqueness of the Robin coefficient on a subpart of the boundary, given Cauchy data on the complementary part, does hold in dimension n=2$n=2$ but needs not hold in higher dimension. We also raise on open issue on harmonic gradients which is of interest in this context.