A uniqueness theorem for determining conductivity from overspecified boundary data
type: Item
instance of: scholarly article
title: A uniqueness theorem for determining conductivity from overspecified boundary data
zbMATH Open document ID: 0666.35078
DOI: 10.1016/0022-247X(88)90112-6
author: William Rundell
author: Michael S. Pilant
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The problem considered is to find the unknown coefficient k(u) in the nonlinear elliptic equation \[ \nabla (k(u)\nabla u)=f(x,y)\quad (x,y)\in \Omega \] with some overspecified boundary condition on a part of the boundary of the bounded domain \(\Omega\). The author shows that this inverse problem can be reduced to solving a linear singular integral equation and that under certain conditions the solution is unique.
reviewed by: Ding Hua
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 4090071
zbMATH Keywords: unknown coefficient
zbMATH Keywords: overspecified boundary condition
zbMATH Keywords: singular integral equation
zbMATH Keywords: unique
MaRDI profile type: Publication
cites work: Determination of the unknown coefficient \(k(u)\) in the equation \(\nabla\cdot k(u)\nabla u = 0\) from overspecified boundary data
cites work: An Inverse Problem for a Nonlinear Diffusion Equation
cites work: Unicity in an inverse problem for an unknown reaction term in a reaction- diffusion equation
cites work: Detection of Mines by Electric Measurements
cites work: Q4040640
cites work: Determining conductivity by boundary measurements II. Interior results
cites work: An Inverse Problem for a Nonlinear Elliptic Differential Equation
cites work: A global uniqueness theorem for an inverse boundary value problem
description: scientific article; zbMATH DE number 4090071