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The stability for the Cauchy problem for elliptic equations

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arxiv 0907.2882 v1 pith:OLP7ECCF submitted 2009-07-16 math.AP

Giovanni Alessandrini , Luca Rondi , Edi Rosset , Sergio Vessella This is my paper · ORCID
classification math.AP
keywords ellipticequationsstabilitycauchyproblemresultsargumentsassumptions
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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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