About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 44, Issue: 4, page 715-735
- ISSN: 0764-583X
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topBourgeois, Laurent. "About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains." ESAIM: Mathematical Modelling and Numerical Analysis 44.4 (2010): 715-735. <http://eudml.org/doc/250773>.
@article{Bourgeois2010,
abstract = {
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with C1,1 boundary. It is an extension of an
earlier result of [Phung, ESAIM: COCV9 (2003) 621–635] for domains of class C∞. Our estimate is established by using a Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Furthermore, we prove that this stability estimate is nearly optimal and induces a nearly optimal convergence rate for the method of quasi-reversibility introduced in [Lattès and Lions, Dunod (1967)] to solve the ill-posed Cauchy problems.
},
author = {Bourgeois, Laurent},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Carleman estimate; distance function; elliptic Cauchy problems; conditional stability; quasi-reversibility},
language = {eng},
month = {6},
number = {4},
pages = {715-735},
publisher = {EDP Sciences},
title = {About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains},
url = {http://eudml.org/doc/250773},
volume = {44},
year = {2010},
}
TY - JOUR
AU - Bourgeois, Laurent
TI - About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/6//
PB - EDP Sciences
VL - 44
IS - 4
SP - 715
EP - 735
AB -
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with C1,1 boundary. It is an extension of an
earlier result of [Phung, ESAIM: COCV9 (2003) 621–635] for domains of class C∞. Our estimate is established by using a Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Furthermore, we prove that this stability estimate is nearly optimal and induces a nearly optimal convergence rate for the method of quasi-reversibility introduced in [Lattès and Lions, Dunod (1967)] to solve the ill-posed Cauchy problems.
LA - eng
KW - Carleman estimate; distance function; elliptic Cauchy problems; conditional stability; quasi-reversibility
UR - http://eudml.org/doc/250773
ER -
References
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