Displaying similar documents to “Optimal stability for inverse elliptic boundary value problems with unknown boundaries”

Unique continuation from Cauchy data in unknown non-smooth domains

Luca Rondi (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We perform measurements of current and voltage type on a (known) part of the boundary of the conductor. We prove that, even if the defects are unknown, the current and voltage measurements at the boundary uniquely determine the corresponding electrostatic potential inside the conductor. A corresponding stability result, related to the stability of Neumann...

Locating the boundary peaks of least-energy solutions to a singularly perturbed Dirichlet problem

Teresa D’Aprile (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider the problemwhere Ω ⊂ ℝ 3 is a smooth and bounded domain, ε , γ 1 , γ 2 > 0 , v , V : Ω → ℝ , f : ℝ → ℝ . We prove that this system has a v ε which develops, as ε → 0 + , a single spike layer located near the boundary, in striking contrast with the result in [37] for the single Schrödinger equation. Moreover the unique peak approaches thepart of ∂ Ω ,, where the boundary mean curvature assumes its maximum. Thus this elliptic system, even though it is a Dirichlet problem, acts more like a Neumann problem...