Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities
By Katya Krupchyk, Gunther Uhlmann. Mathematical Research Letters, 2019
86 citations recorded by the source corpus.
We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain $\Omega\subset \mathbb{R}^n$ which vanish on a closed proper subset of the boundary is dense in $L^1(\Omega)$. We apply this density result to solve some partial data inverse boundary problems for a class of semilinear elliptic PDE with quadratic gradient terms.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/34c064d77bb3e70da41a4c7823fcce7d35a6a7f9
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In Applied Mathematics
- Katya Krupchyk
- Gunther Uhlmann
- Yavar Kian
- Ali Feizmohammadi
- C. Carstea
- Mikko Salo
- Plamen Stefanov
- Victor Isakov
In Computational Theory and Mathematics
- Katya Krupchyk
- Gunther Uhlmann
- Ali Feizmohammadi
- Yavar Kian
- C. Carstea
- Mikko Salo
- Plamen Stefanov
- Matti Lassas
In Mathematical Physics
- Katya Krupchyk
- Gunther Uhlmann
- Ali Feizmohammadi
- Yavar Kian
- C. Carstea
- Mikko Salo
- Plamen Stefanov
- Matti Lassas
Citations in the corpus
- 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.”