Dirichlet's problem in banach space
Copyright policy )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).
- Lomonosov Moscow State University Russian Federation
Probability theory on algebraic and topological structures, Diffusion processes, diffusion processes in Banach space, Stochastic ordinary differential equations (aspects of stochastic analysis), Dirichlet problem
Probability theory on algebraic and topological structures, Diffusion processes, diffusion processes in Banach space, Stochastic ordinary differential equations (aspects of stochastic analysis), Dirichlet problem
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