Displaying similar documents to “Boundary trace of positive solutions of nonlinear elliptic inequalities”

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 ≥ 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.

An overdetermined elliptic problem in a domain with countably rectifiable boundary

Przemysław Górka (2007)

Colloquium Mathematicae

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We examine an elliptic equation in a domain Ω whose boundary ∂Ω is countably (m-1)-rectifiable. We also assume that ∂Ω satisfies a geometrical condition. We are interested in an overdetermined boundary value problem (examined by Serrin [Arch. Ration. Mech. Anal. 43 (1971)] for classical solutions on domains with smooth boundary). We show that existence of a solution of this problem implies that Ω is an m-dimensional Euclidean ball.

The transmission problem with boundary conditions given by real measures

Dagmar Medková (2007)

Annales Polonici Mathematici

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The unique solvability of the problem Δu = 0 in G⁺ ∪ G¯, u₊ - au_ = f on ∂G⁺, n⁺·∇u₊ - bn⁺·∇u_ = g on ∂G⁺ is proved. Here a, b are positive constants and g is a real measure. The solution is constructed using the boundary integral equation method.

Some possibly degenerate elliptic problems with measure data and non linearity on the boundary

Thierry Gallouët, Yannick Sire (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two types of problems: the first one deals with the laplacian in a bounded domain with measure supported on the domain and on the boundary. A second one deals with the same type of data but involves a degenerate weight in the equation. In both cases, the nonlinearity under consideration lies on the boundary. For the...

Martin boundary and positive solutions of some boundary value problems

Evgeny B. Dynkin (1965)

Annales de l'institut Fourier

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Nous étudions le problème de Neumann avec dérivée oblique dans un domaine 2-dimensionnel borné par un contour régulier C . Le champ vectoriel donné sur C peut être tangent à C en un nombre fini de points. En utilisant une extension de la méthode de Martin nous trouvons toutes les solutions positives de ce problème aux valeurs limites.