Unique continuation from Cauchy data in unknown non-smooth domains

Luca Rondi

Displaying similar documents to “Unique continuation from Cauchy data in unknown non-smooth domains”

A note on the Rellich formula in Lipschitz domains.

Alano Ancona (1998)

Publicacions Matemàtiques

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Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain Ω of R and having Lipschitz coefficients in Ω. It is shown that the Rellich formula with respect to Ω and L extends to all functions in the domain D = {u ∈ H (Ω); L(u) ∈ L(Ω)} of L. This answers a question of A. Chaïra and G. Lebeau.

Optimal stability for inverse elliptic boundary value problems with unknown boundaries

Giovanni Alessandrini, Elena Beretta, Edi Rosset, Sergio Vessella (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On the Poisson integral for Lipschitz and $C^{1}$ -domains

Björn Dahlbert (1979)

Studia Mathematica

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Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains

Carlos E. Kenig (1983-1984)

Séminaire Équations aux dérivées partielles (Polytechnique)

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Fatou theorems for some nonlinear elliptic equations.

Eugene Fabes, Nicola Garofalo, Santiago Marin Malave, Sandro Salsa (1988)

Revista Matemática Iberoamericana

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An endpoint Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains.

Pascal Auscher, Philippe Tchamitchian (1999)

Publicacions Matemàtiques

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We prove a commutator inequality of Littlewood-Paley type between partial derivatives and functions of the Laplacian on a Lipschitz domain which gives interior energy estimates for some BVP. It can be seen as an endpoint inequality for a family of energy estimates.

Boundary behavior of subharmonic functions in nontangential accessible domains

Shiying Zhao (1994)

Studia Mathematica

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The following results concerning boundary behavior of subharmonic functions in the unit ball of $ℝ^{n}$ are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek’s theorem on the $L^{p}$ -nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.

Area integral estimates for higher order elliptic equations and systems

Björn E. J. Dahlberg, Carlos E. Kenig, Jill Pipher, G. C. Verchota (1997)

Annales de l'institut Fourier

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Let $L$ be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in $L^{p}$ norm between the maximal function and the square function of solutions to $L$ in Lipschitz domains. Several applications of this result are discussed.