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A new type boundary value problem for the wave equation. (English. Russian original) Zbl 0839.35071
Russ. Acad. Sci., Dokl., Math. 49, No. 3, 564-567 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 5, 590-591 (1994).
By the method of a priori estimates the author proves the unique solvability of certain problems for the wave equation. The Dirichlet problem is one of them. The existence theorem and a priori estimate are proved in the Sobolev space $$W_2^1$$ with a weight.
##### MSC:
 35L05 Wave equation 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B45 A priori estimates in context of PDEs
##### Keywords:
weighted Sobolev space; unique solvability