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• W1503991963 abstract "Given a general symmetric elliptic operator $$ L_{a} := sum_{k,,j=1}^d p_k (a_{kj} p_j) + sum_{k=1}^d a_k p_k - p_k(overline{a_k} .) + a_0$$we define the associated Dirichlet-to-Neumann (D-t-N) operator with partial data, i.e., data supported in a part of the boundary. We prove positivity, $L^p$-estimates and domination properties for the semigroup associated with this D-t-N operator. Given $L_a $ and $L_b$ of the previous type with bounded measurable coefficients $a = {a_{kj}, a_k, a_0 }$ and $b = {b_{kj}, b_k, b_0 }$, we prove that if their partial D-t-N operators (with $a_0$ and $b_0$ replaced by $a_0 -la$ and $b_0 -la$) coincide for all $la$, then the operators $L_a$ and $L_b$, endowed with Dirichlet, mixed or Robin boundary conditions are unitary equivalent. In the case of the Dirichlet boundary conditions, this result was proved recently by Behrndt and Rohleder cite{BR12} for Lipschitz continuous coefficients. We provide a different proof which works for bounded measurable coefficients and other boundary conditions." @default.
• W1503991963 created "2016-06-24" @default.
• W1503991963 creator A5087792269 @default.
• W1503991963 date "2015-01-29" @default.
• W1503991963 modified "2023-09-25" @default.
• W1503991963 title "A milder version of Calder'on's inverse problem for anisotropic conductivities and partial data" @default.
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