# 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 -

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