In this paper we obtain quantitative estimates of strong unique continuation for solutions to parabolic equations. We apply these results to prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain Omega in R(n), from the knowledge of overdetermined boundary data for parabolic boundary value problems.
QUANTITATIVE ESTIMATES OF UNIQUE CONTINUATION FOR PARABOLIC EQUATIONS AND INVERSE-INITIAL BOUNDARY VALUE PROBLEM WITH UNKNOWN BOUNDARIES / B. CANUTO; E. ROSSET; S. VESSELLA. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 354:(2002), pp. 491-535. [10.1090/S0002-9947-01-02860-4]
QUANTITATIVE ESTIMATES OF UNIQUE CONTINUATION FOR PARABOLIC EQUATIONS AND INVERSE-INITIAL BOUNDARY VALUE PROBLEM WITH UNKNOWN BOUNDARIES
VESSELLA, SERGIO
2002
Abstract
In this paper we obtain quantitative estimates of strong unique continuation for solutions to parabolic equations. We apply these results to prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain Omega in R(n), from the knowledge of overdetermined boundary data for parabolic boundary value problems.
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