A remark on partial data inverse problems for semilinear elliptic equations

By Katya Krupchyk, Gunther Uhlmann. Proceedings of the American Mathematical Society, 2019

111 citations recorded by the source corpus.

We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a017dc59916818c15be2ab90b2e7da0c10b3fe6c

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities (2019, methodology): “e Caldero´n inverse problem with partial data, see [24] and [40] for review, and it provides the solution of the linearized version of the partial data problem at the zero potential. The recent works [27] and [30] have exploited this density result to give a solution for the partial data inverse bou”
The Calderón inverse problem for isotropic quasilinear conductivities (2021, background): “Without being exhaustive, we mention also the works of [6, 9, 10, 7, 8] devoted to the recovery of similar type of nonlinear terms for certain classes of elliptic nonlinear equations and the works of [13, 29, 30, 31, 35, 36, 37, 33] devoted to inverse problems for semilinear elliptic equations.”