An inverse problem for an elliptic equation with an affine term
type: Item
instance of: scholarly article
title: An inverse problem for an elliptic equation with an affine term
zbMATH Open document ID: 0958.35021
author: Robert Dalmasso
published in: Mathematische Annalen
publication date: 2001-04-02T00:00:00Z
review text: The author proves that for a large class of planar domains \(\Omega\) (including all true ellipses) and any real-valued \(\psi\in C^\infty (\partial \Omega)\) which is not identically constant there exist at most \(k_0\) different pairs of coefficients \((\lambda_k,\mu_k) \in\mathbb{R}^2\) such that the Cauchy problem \[ \Delta u=-\lambda_k u-\mu_k\text{ in }\Omega,\quad u=0, {\partial u\over \partial n}=\psi\text{ on }\partial\Omega \] has a solution. The numbers \(k_0\), \(\lambda_k\), and \(\mu_k\) are explicitly computable.
reviewed by: Ralf Beyerstedt
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 1463214
zbMATH Keywords: elliptic equation
zbMATH Keywords: inverse problem
MaRDI profile type: Publication
full work available at URL: s002080050354
OpenAlex ID: W2073848015
DOI: 10.1007/S002080050354
description: scientific article; zbMATH DE number 1463214