The Calderón problem for quasilinear elliptic equations
By Claudio Muñoz, Gunther Uhlmann. 2020
47 citations recorded by the source corpus.
Abstract In this paper we show uniqueness of the conductivity for the quasilinear Calderon's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions on the direct problem, a real-valued conductivity allowing a small analytic continuation to the complex plane induce a unique Dirichlet-to-Neumann (DN) map. The method of proof considers some complex-valued, linear test functions based on a point of the boundary of the domain, and a linearization of the DN map placed at these particular set of solutions.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/957865958a71c8f657894ef831905561d0ba91f9
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In Computational Theory and Mathematics
- Katya Krupchyk
- Gunther Uhlmann
- Mikko Salo
- Plamen Stefanov
- Matti Lassas
- Carlos E. Kenig
- David dos Santos Ferreira
- Venkateswaran P. Krishnan
In Mathematical Physics
- Katya Krupchyk
- Gunther Uhlmann
- Mikko Salo
- Plamen Stefanov
- Matti Lassas
- Yi-Hsuan Lin
- David dos Santos Ferreira
- Carlos E. Kenig
In Mechanics of Materials
Citations in the corpus
- A remark on partial data inverse problems for semilinear elliptic equations (2019, methodology): “ finally mention that inverse problems for nonlinear elliptic PDE have been studied extensively, both in the semilinear setting, see [7], [8], [9], [18], as well as the quasilinear one, see [1], [10], [15], [16], [17]. In particular, the second order linearization of the nonlinear Dirichlet–to–Neuman”
- Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities (2019, methodology): “oblem when n= 2, (iv) ∇ · (γ(x,u)∇u) = 0, see [41], [44] for the full data problem in the case n≥ 2, (v) ∇·( → C(x,∇u)) = 0, see [5], [23], [12] for the full data problem, (vi) ∇·(c(u,∇u)∇u) = 0, see [37] for the full data problem when n≥ 2. A classical method for attacking inverse boundary problems”
- An inverse problem for a semi-linear elliptic equation in Riemannian geometries (2019, unknown): “Aside from the study of inverse problems for semi-linear equations in Euclidean geometries, let us also mention that there are several works related to inverse problems for quasi-linear elliptic equations (see for example [3, 10, 17, 32, 39, 40, 41]).”