English

Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities

Analysis of PDEs 2019-09-19 v1

Abstract

We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain ΩRn\Omega\subset \mathbb{R}^n which vanish on a closed proper subset of the boundary is dense in L1(Ω)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.

Keywords

Cite

@article{arxiv.1909.08122,
  title  = {Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities},
  author = {Katya Krupchyk and Gunther Uhlmann},
  journal= {arXiv preprint arXiv:1909.08122},
  year   = {2019}
}
R2 v1 2026-06-23T11:18:35.490Z