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Rigidity of inverse problems for nonlinear elliptic equations on manifolds
- Publication Year :
- 2023
-
Abstract
- We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative answer to this problem. Owing to this obstruction, we consider a new formulation of our inverse problem in terms of a rigidity problem. Precisely, we consider cases where the Dirichlet-to-Neumann map of a semilinear equation coincides with the one of a linear equation and ask whether this implies that the equation must indeed be linear. We give a positive answer to this rigidity problem under some assumptions imposed to the Riemannian manifold and to the semilinear term under consideration.
- Subjects :
- Mathematics - Analysis of PDEs
35R30, 35J91
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2306.05839
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1112/blms.13102