Single Measurement Detection Of a Discontinuous Conductivity
- 1 January 1990
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 15 (4) , 153-169
- https://doi.org/10.1080/03605309908820695
Abstract
Let be a bounded region in R$sup:n$esup: 2. with C$sup:2$esup: boundary and conductivity ggr;Suppose that some region D CC may have been replaced with a material which has a differing C$sup:2$esup: conductivity profile. We show that by applying an appropriate current flux on and measuring the resulting potential on an open subset one can "detect" the presence of the region D, that is. the potentials induced on when D is present versus absent must differ. Moreover. if D and its conductivity are known to satisfy certain a priori restrictions, one can assert that the potentials induced on must differ by a fixed aount which does not depend on the domain D or its conductivity.Keywords
This publication has 8 references indexed in Scilit:
- Elliptic Partial Differential Equations of Second OrderPublished by Springer Nature ,2001
- On uniqueness of recovery of a discontinuous conductivity coefficientCommunications on Pure and Applied Mathematics, 1988
- Inverse boundary value problems at the boundary—continuous dependenceCommunications on Pure and Applied Mathematics, 1988
- Detection of Mines by Electric MeasurementsSIAM Journal on Applied Mathematics, 1987
- A Global Uniqueness Theorem for an Inverse Boundary Value ProblemAnnals of Mathematics, 1987
- Determining conductivity by boundary measurementsCommunications on Pure and Applied Mathematics, 1984
- Introduction to Partial Differential EquationsPublished by Walter de Gruyter GmbH ,1976
- Partial Differential Equations of Elliptic TypePublished by Springer Nature ,1970