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INICIO | 17 de abril de 2024

On the boundary values of harmonic functions.

Título inglés On the boundary values of harmonic functions.
Título español Sobre los valores en la frontera de las funciones armónicas.
Autor/es Garabedian, Paul R.
Organización Courant Inst. Math. Sci. New York Univ., Nueva York, Estados Unidos
Revista 0213-2230
Publicación 1985, 1 (2): 33-37, 5 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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 Dirichlet integral [5]. Here a problem has remained open concerning continuity at the boundary of the solution that is constructed by orthogonal projection. Past discussion of this question turned out to be successful in spaces of two or three dimensions, but failed for larger numbers of independent variables [2]. It is the purpose of the present note to remove any such restriction and simultaneously to give a concise treatment of the boundary condition that is applicable to other existence proofs.
Clasificación UNESCO 120220
Palabras clave español Ecuación de Laplace ; Función de Green ; Función armónica
Código MathReviews MR0850684
Código Z-Math Zbl 0602.31005
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)