On interior regularity of solutions of a class ofalmost-hypoelliptic equations

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On interior regularity of solutions of a class ofalmost-hypoelliptic equations Hayk Ghazaryan

In this paper it is proved that all distributional solutions of the non-degenerate, al-most hypoelliptic (hypoelliptic by the one of variables) equation푃(퐷)푢=푃(퐷1,퐷2)푢=0are infinitely differentiable in the certain strip in퐸2under a priori assumption thatthey and its certain derivatives are square integrable with a certain exponential weight.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/71 Armenian Journal of Mathematics, 3(2) 32-60

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Keywords

hypoelliptic in respect to a group of variables operator, almost - hypoellipticoperator, weighted Sobolev spaces

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