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Zeitschrift für Analysis und ihre Anwendungen

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Volume 17, Issue 4, 1998, pp. 1021–1024
DOI: 10.4171/ZAA/864

Published online: 1998-12-31

Domain Identification for a Nonlinear Elliptic Equation

Dang Duc Trong[1]

(1) National University, Hochiminh City, Vietnam

It is proposed to identify the domain $\Omega \in \mathbb R^n$ of a nonlinear elliptic equation subject to given Cauchy data on part of the known outer boundary $\Gamma$ and to the zero condition on the unknown inner boundary $\gamma$. It is proved that under the assumption $\dot{\bar{\Omega}} = \Omega$, the domain $\Omega$ is uniquely determined.

Keywords: Domain identification, nonlinear elliptic equations, zero Dirichiet condition

Trong Dang Duc: Domain Identification for a Nonlinear Elliptic Equation. Z. Anal. Anwend. 17 (1998), 1021-1024. doi: 10.4171/ZAA/864