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Partial Data Inverse Problems for Semilinear Elliptic Equations with Gradient Nonlinearities by Krupchyk, Katya; Uhlmann, Gunther is a scholarly article available to read on EtoBox.

What is Partial Data Inverse Problems for Semilinear Elliptic Equations with Gradient Nonlinearities about?

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.

Author

Krupchyk, Katya; Uhlmann, Gunther

Published

2019

Language

EN