Inverse problems in the ”large” and Carleman bounds. (English. Russian original) Zbl 0573.35083

Klibanov, M. V.

Differ. Equations 20, 755-760 (1984); translation from Differ. Uravn. 20, No. 6, 1035-1041 (1984).

The author suggests a new method of investigation of a large class of inverse problems for differential equations. The method is based on the reduction of the inverse problem to an integro-differential inequality to which a weighted a priori estimate of Carleman type is applied. The method does not depend upon type or order of the equation and assumes only the availability of a Carleman estimation; in order to prove this, examples are given.

Reviewer: C.Simionescu

MSC:

35R30	Inverse problems for PDEs
35B45	A priori estimates in context of PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

uniqueness; conditional stability; reduction; integro-differential inequality; a priori estimate of Carleman type