Year: 1995
Type: article
Abstract: We prove local uniqueness of a domain $D$ entering the conductivity equation ${\text {div}}((1 + \chi (D))\nabla u) = 0$ in a bounded planar domain $\Omega$ given the Cauchy data for $u$ on a part of $\partial \Omega$. The main assumption is that $\nabla u$ has zero index on $\partial \Omega$ which is easy to guarantee by choosing special boundary data for $u$. To achieve our goals we study index of critical points of $u$ on $\partial \Omega$.
Authors: G. Alessandrini, V. Isakov, J. Powell
Institution: Wichita State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G1702950523, G3906074002
OpenAlex ID: W2056972463