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Some boundary value problems for elliptic equations, and Lie algebras connected with them. II. (Russian) Zbl 0658.35028

[For part I see Mat. Sb., Nov. Ser. 126(168), No.2, 215-246 (1985; Zbl 0589.35035).]
The author considers boundary value problems for second order linear elliptic differential equations with smooth coefficients in a bounded domain \(\Omega \subset R^{n+1}\) with smooth boundary M where the boundary condition is defined by a second order differential operator such that Lopatinski’s conditions are not satisfied on a rather arbitrary subset of M. This paper is the continuation of a previous work of the author with the same title. In contrary to that work, here the main part of the boundary operator is not supposed to be definite and so the kernel and the cokernel of the problem may be of infinite dimension. There are given additional boundary conditions on a submanifold of the boundary such that the boundary value problem will be correctly posed. It is also shown that usual results on global regularity of solutions U of elliptic problems are not true in general but some additional conditions imply e.g. \(U\in C^{\infty}({\bar \Omega})\).
Reviewer: L.Simon

MSC:

35J25 Boundary value problems for second-order elliptic equations
35R25 Ill-posed problems for PDEs
35B65 Smoothness and regularity of solutions to PDEs

Citations:

Zbl 0589.35035
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