Boundary value problems for quasielliptic equations in a half-space

V. S. Belonosov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We consider general boundary value problems with data on the boundary of a half-space for quasielliptic equations with constant coefficients. We find integral representations for solutions and study some properties of the kernels of the corresponding integral operators. The results are applied to proving some generalization of the Miranda–Agmon maximum principle.

Keywords: quasielliptic equation, boundary value problem, Poisson kernel, maximum principle.

UDC: 517.95

Received: 25.04.2005

 English version: Siberian Mathematical Journal, 2005, 46:5, 783–795

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