Remark on a certain theorem of H.J. Bremermann

J. Górski

Displaying similar documents to “Remark on a certain theorem of H.J. Bremermann”

Convexity and uniqueness in a free boundary problem arising in combustion theory.

Arshak Petrosyan (2001)

Revista Matemática Iberoamericana

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We consider solutions to a free boundary problem for the heat equation, describing the propagation of flames. Suppose there is a bounded domain Ω ⊂ Q_T = Rⁿ x (0,T) for some T > 0 and a function u > 0 in Ω such that u_t = Δu, in Ω, u = 0 and |∇u| = 1, on Γ := ∂Ω ∩ Q_T, u(·,0) = u₀, on Ω₀, ...

On the boundary values of harmonic functions.

Paul R. Garabedian (1985)

Revista Matemática Iberoamericana

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Over the years many methods have been discovered to prove the existence of a solution of the Dirichlet problem for Laplace's equation. A fairly recent collection of proofs is based on representations of the Green's functions in terms of the Bergman kernel function or some equivalent linear operator [3]. Perhaps the most fundamental of these approaches involves the projection of an arbitrary function onto the class of harmonic functions in a Hilbert space whose norm is defined by 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.

Dirichlet problem with L $^{p}$ -boundary data in contractible domains of Carnot groups

Andrea Bonfiglioli, Ermanno Lanconelli (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $ℒ$ be a sub-laplacian on a stratified Lie group $G$ . In this paper we study the Dirichlet problem for $ℒ$ with $L^{p}$ -boundary data, on domains $Ω$ which are contractible with respect to the natural dilations of $G$ . One of the main difficulties we face is the presence of non-regular boundary points for the usual Dirichlet problem for $ℒ$ . A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.

Boundary properties of functions with finite Dirichlet integrals

J. L. Doob (1962)

Annales de l'institut Fourier

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L’auteur étudie dans un espace de Green (en particulier un domaine borné de $R^{n}$ ) les fonctions $B L D$ (limites en un certain sens des fonctions assez régulières à intégrale de Dirichlet finie). On se ramène au cas harmonique montré qu’une telle fonction harmonique $u$ est solution d’un problème de Dirichlet-Martin (c’est-à-dire correspond à une donnée $u^{'}$ sur la frontière de Martin), ce qui entraîne l’existence d’une limite “fine” $u^{'}$ p.p. Cela résulte de travaux antérieurs et de la remarque que...

Solutions with prescribed periods on the boundary components on non-linear elliptic systems of first order in multiply connected domains in the plane

Wolfgang Tutschke (1983)

Banach Center Publications

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Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation — and vice-versa

Keith Miller (1968)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Displaying similar documents to “Remark on a certain theorem of H.J. Bremermann”

Convexity and uniqueness in a free boundary problem arising in combustion theory.

On the boundary values of harmonic functions.

Martin boundary and positive solutions of some boundary value problems

Dirichlet problem with L p -boundary data in contractible domains of Carnot groups

Boundary properties of functions with finite Dirichlet integrals

Solutions with prescribed periods on the boundary components on non-linear elliptic systems of first order in multiply connected domains in the plane

Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation — and vice-versa

Dirichlet problem with L $^{p}$ -boundary data in contractible domains of Carnot groups