The stability for the Cauchy problem for elliptic equations

Details The stability for the Cauchy problem for elliptic equations The stability for the Cauchy problem for elliptic equations

2009-07-16

arxiv.org/abs/0907.2882v1

Inverse Problems 25 123004, 2009, (47pp)

Mathematics

Analysis of PDEs

57 pages, review article

Scientific paper

10.1088/0266-5611/25/12/123004

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.

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