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Extension of solutions in domains with piecewise-analytic boundaries. (English. Russian original) Zbl 0885.35018
Dokl. Math. 51, No. 2, 177-179 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 341, No. 1, 24-27 (1995).
The authors study the problem of the extension of some solutions to homogeneous elliptic differential equations originally given in domains with piecewise-algebraic boundary. They consider the solutions that appear in the balayage problem and the boundary value problem. Discussing the general case, they formulate two theorems for special plane domains. The authors construct Riemannian surfaces for extended functions. In the second theorem, they give the reflection formula for the continuation of the solution.
35B60 Continuation and prolongation of solutions to PDEs
35J30 Higher-order elliptic equations
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions