Displaying similar documents to “The theory of small changesin the domain of existence in the theory of partial differential equations and its applications”

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...