An overdetermined elliptic problem in a domain with countably rectifiable boundary

Przemysław Górka

Displaying similar documents to “An overdetermined elliptic problem in a domain with countably rectifiable boundary”

On the boundary domains of the n-th eigenfunctions for the self-adjoined elliptic equation

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ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order ε in the energy norm.

Boundary trace of positive solutions of nonlinear elliptic inequalities

Moshe Marcus, Laurent Véron (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of $- Δ u + g (x, u) \geq 0$ in a smooth domain $Ω$ under very general assumptions on $g$ . This new definition which extends the previous notions of boundary trace is based upon a sweeping technique by solutions of Dirichlet problems with measure boundary data. We also prove a boundary pointwise blow-up estimate of any solution of such inequalities in terms of the Poisson kernel. If the...

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Devdariani, G. (2001)

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We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.

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Andrzej Czarnecki, Marcin Kulczycki, Wojciech Lubawski (2011)

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This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.

Boundary trace of solutions of semilinear elliptic equalities and inequalities

Laurent Véron (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The boundary trace problem for positive solutions of $- △ u + g (x, u) \geq 0$ is considered for nonlinearities of absorption type, and three different methods for defining the trace are compared. The boundary trace is obtained as a generalized Borel measure. The associated Dirichlet problem with boundary data in the set of such Borel measures is studied.