This article is cited in 5 papers

On certain generalizations of the Dirichlet problem

Yu. A. Rozanov


Abstract: A characterization is given of boundary conditions for linear differential operators in a domain with arbitrary boundary, and these conditions are used to state a boundary-value problem in a suitable function class. It is proved that this “generalized Dirichlet problem” has a unique solution which depends continuously on the boundary conditions.
Bibliography: 3 titles.

UDC: 517.544

MSC: Primary 35A05, 35D05, 35G15, 35B30; Secondary 31B20, 46E35, 44F05, 60G60, 60J99

Received: 22.04.1982

 English version: Mathematics of the USSR-Sbornik, 1984, 48:2, 287–305

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