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Solutions of the membrane equation concentrated near extremal loops. (English. Russian original) Zbl 0900.35115

J. Math. Sci., New York 91, No. 2, 2725-2732 (1998); translation from Zap. Nauchn. Semin. POMI 230, 41-51 (1995).
Summary: Formal asymptotic solutions of the equation \(\Delta^2u- (\omega^4/c^4(x,y))u=0\) concentrated near extremal cycles with \(N\geq 2\) corners are constructed by application of the complex ray method.

MSC:

35J30 Higher-order elliptic equations
35C20 Asymptotic expansions of solutions to PDEs
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References:

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