Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities

Katya Krupchyk; Gunther Uhlmann

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arXiv · 1909.08122

Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities

Katya Krupchyk·Gunther Uhlmann

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Abstract

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.

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Katya Krupchyk, Gunther Uhlmann. 2019-09-17. Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities. https://arxiv.org/abs/1909.08122

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