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NEW GLOBAL LOGARITHMIC STABILITY RESULTS ON THE CAUCHY PROBLEM FOR ELLIPTIC EQUATIONS

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  18 July 2019

MOURAD CHOULLI Open the ORCID record for MOURAD CHOULLI [Opens in a new window]
MOURAD CHOULLI*
Affiliation:
Université de Lorraine, 34 cours Léopold, 54052 Nancy cedex, France email mourad.choulli@univ-lorraine.fr
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Abstract

We prove the global logarithmic stability of the Cauchy problem for $H^{2}$-solutions of an anisotropic elliptic equation in a Lipschitz domain. The result is based on existing techniques used to establish stability estimates for the Cauchy problem combined with related tools used to study an inverse medium problem.

Keywords

elliptic equationCauchy problemglobal logarithmic stability

MSC classification

Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 141 - 145
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

The author is supported by grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde).

References

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