Dirichlet's problem in Banach space
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).
scientific article; zbMATH DE number 3860111