Displaying similar documents to “Boundary trace of solutions of semilinear elliptic equalities and inequalities”

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 ) ≥ 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...

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.

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.

Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos (2004)

Annales Polonici Mathematici

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We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.

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.