Mathematics

On a solutions of one class of almost hypoelliptic equations

G. H. Hakobyan

Yerevan State University

Abstract: We prove, that if $P(D)=P(D_1,D_2)=\sum_{\alpha}\gamma_{\alpha} D_1^{\alpha_1}D_2^{\alpha_2}$ is an almost hypoelliptic regular operator, then for enough small $\delta>0$ all the solutions of the equation $P(D)u = 0$ from $L_{2,\delta} (R^2)$ are entire analytical functions.

Keywords: almost hypoelliptic operator (polynom), weighted Sobolev spaces, analyticity of solution.

MSC: 42B08

Received: 24.11.2014
Accepted: 25.12.2014

Language: English