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Selfadjoint extensions of the Dirichlet problem operator in weighted function spaces. (English. Russian original) Zbl 0683.35033

Math. USSR, Sb. 65, No. 1, 229-247 (1990); translation from Mat. Sb., Nov. Ser. 137(179), No. 2(10), 224-241 (1988).
The author considers the Dirichlet boundary value problem for a formally self-adjoint elliptic system in the sense of Petrowskij in certain weighted function spaces. He applies and specifies known results concerning general singular elliptic boundary value problems due to V. A. Kondratev [Tr. Mosk. Mat. O.-Va 16, 209-292 (1967; Zbl 0162.163)] and V. G. Maz’ja and B. A. Plamenevskij [Math. Nachr. 76, 29- 60 (1977; Zbl 0359.35024)]. Generalizing a method of Yu. E. Karpeshina and B. S. Pavlov [Math. Notes 40, 528-533 (1986); translation from Mat. Zametki 40, No.1, 49-59 (1986; Zbl 0641.35022)] he describes all self-adjoint extensions of the operaor related to this boundary value problem in the space \(L_ 2\) with the weight \(| x|^{2\sigma}\). Some special examples and some variants of the considered problem are given.
Reviewer: M.Goebel

MSC:

35J70 Degenerate elliptic equations
47B25 Linear symmetric and selfadjoint operators (unbounded)
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