Analysis & PDE

  • Anal. PDE
  • Volume 6, Number 7 (2013), 1601-1648.

Carleman estimates for anisotropic elliptic operators with jumps at an interface

Jérôme Le Rousseau and Nicolas Lerner

Full-text: Open access

Abstract

We consider a second-order self-adjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight function such that a Carleman estimate holds true. We also prove that the conditions imposed on the weight function are sharp.

Article information

Source
Anal. PDE, Volume 6, Number 7 (2013), 1601-1648.

Dates
Received: 31 January 2012
Revised: 8 March 2013
Accepted: 13 April 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731431

Digital Object Identifier
doi:10.2140/apde.2013.6.1601

Mathematical Reviews number (MathSciNet)
MR3148062

Zentralblatt MATH identifier
1319.47038

Subjects
Primary: 35J15: Second-order elliptic equations 35J57: Boundary value problems for second-order elliptic systems 35J75: Singular elliptic equations

Keywords
Carleman estimate elliptic operator nonsmooth coefficient quasimode

Citation

Le Rousseau, Jérôme; Lerner, Nicolas. Carleman estimates for anisotropic elliptic operators with jumps at an interface. Anal. PDE 6 (2013), no. 7, 1601--1648. doi:10.2140/apde.2013.6.1601. https://projecteuclid.org/euclid.apde/1513731431


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