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Vishik-Lyusternik method for elliptic boundary-value problems in domains with conical point. III. Problem with degeneracy at a conical point. (English. Russian original) Zbl 0593.35049
Sib. Math. J. 25, 917-925 (1984); translation from Sib. Mat. Zh. 25, No. 6(148), 106-115 (1984).
[For part II see ibid. 22, 753-769 (1982); translation from Sib. Math. Zh. 22, 132-152 (1981; Zbl 0479.35033).]
The author studies elliptic boundary value problems degenerating at a conical point of the boundary into a boundary value problem of lower order. A modified Vishik-Lyusternik method is used for the construction of a boundary layer which is induced by the degeneracy. The problem is formulated as an operator equation in certain weighted spaces. Necessary and sufficient conditions are given under which Noether theorems for the corresponding operator hold.
Reviewer: M.Kučera

35J70 Degenerate elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
Full Text: DOI EuDML
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