Carleman estimates for elliptic operators with complex coefficients Part II: transmission problems

Abstract : We consider elliptic transmission problems with complex coefficients across an interface. Under proper transmission conditions, that extend known conditions for well-posedness, and sub-ellipticity we derive microlocal and local Carleman estimates near the interface. Carleman estimates are weighted a priori estimates of the solutions of the elliptic transmission problem. The weight is of exponential form, exp(τ ϕ) where τ can be taken as large as desired. Such estimates have numerous applications in unique continuation, inverse problems, and control theory. The proof relies on microlocal factorizations of the symbols of the conjugated operators in connection with the sign of the imaginary part of their roots. We further consider weight functions where ϕ = exp(γψ), with γ acting as a second large paremeter, and we derive estimates where the dependency upon the two parameters, τ and γ, is made explicit. Applications to unique continuation properties are given.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [41 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01312627
Contributor : Jérôme Le Rousseau <>
Submitted on : Saturday, May 7, 2016 - 10:12:37 PM
Last modification on : Thursday, April 4, 2019 - 10:18:05 AM
Long-term archiving on: Wednesday, May 25, 2016 - 6:30:11 AM

Files

transmission.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01312627, version 1
  • ARXIV : 1605.02535

Citation

Mourad Bellassoued, Jérôme Le Rousseau. Carleman estimates for elliptic operators with complex coefficients Part II: transmission problems. 2015. ⟨hal-01312627⟩

Share

Metrics

Record views

299

Files downloads

319