Dirichlet's problem in Banach space (Q794342)
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scientific article; zbMATH DE number 3860111
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dirichlet's problem in Banach space |
scientific article; zbMATH DE number 3860111 |
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Dirichlet's problem in Banach space (English)
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1983
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The author investigates a Dirichlet problem for the equation \(Lu=tr A(x)u''(x)A(x)+u'(x)a(x)=-g(x)\) in a region G of a Banach space X with boundary \(\Gamma\). Using a known probability representation of the solution of the problem \(Lu=-g\), \(u|_{\Gamma}=\psi\) he extends some results by \textit{N. N. Frolov} [Teor. Veroyatn. Mat. Stat. 3, 200-210 (1970; Zbl 0248.60042)] to the case of Banach space basing on the results by the reviewer and \textit{Yu. L. Daletskij}, Tr. Mosk. Math. O.-va. 37, 107-141 (1978; Zbl 0432.60078).
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diffusion processes in Banach space
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Dirichlet problem
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