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 which vanish on a closed proper subset of the boundary is dense in . We apply this density result to solve some partial data inverse boundary problems for a class of semilinear elliptic PDE with quadratic gradient terms.
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}
}