Open Access Research

Carleman estimates and unique continuation property for abstract elliptic equations

Veli B Shakhmurov

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Author affiliations

Department of Electronics Engineering and Communication, Okan University, Akfirat Beldesi, Tuzla, 34959, Istanbul, Turkey

Citation and License

Boundary Value Problems 2012, 2012:46 doi:10.1186/1687-2770-2012-46

Published: 23 April 2012

Abstract

The unique continuation theorems for elliptic differential-operator equations with variable coefficients in vector-valued Lp-space are investigated. The operator-valued multiplier theorems, maximal regularity properties and the Carleman estimates for the equations are employed to obtain these results. In applications the unique continuation theorems for quasielliptic partial differential equations and finite or infinite systems of elliptic equations are studied.

AMS: 34G10; 35B45; 35B60.

Keywords:
Carleman estimates; unique continuation; embedding theorems; Banach-valued function spaces; differential operator equations; maximal Lp-regularity; operator-valued Fourier multipliers; interpolation of Banach spaces