Dirichlet's problem in Banach space
type: Item
instance of: scholarly article
title: Dirichlet's problem in Banach space
zbMATH Open document ID: 0541.60054
DOI: 10.1007/BF01157401
published in: Mathematical Notes
publication date: 1983-01-01T00:00:00Z
review text: 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).
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60B99
zbMATH DE Number: 3860111
zbMATH Keywords: diffusion processes in Banach space
zbMATH Keywords: Dirichlet problem
author: Andrei Khrennikov
MaRDI profile type: Publication
cites work: Potential theory on Hilbert space
cites work: Stochastic integrals in abstract Wiener space
cites work: Q3924581
cites work: Q5642761
cites work: Q3657121
cites work: Q4081425
cites work: Q5664372
description: scientific article; zbMATH DE number 3860111