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On the smoothness of solutions of a class of regular equations in a strip

Research paper by S. R. Hayrapetyan

Indexed on: 01 Sep '10Published on: 01 Sep '10Published in: Journal of Contemporary Mathematical Analysis



Abstract

The paper considers a class of regular, hypoelliptic in x1, two-dimensional operators P(D) = P(D1,D2) in rather wide strip ΩH = {x = (x1; x2) ∈ \( \mathbb{E} \)2, |x1| < H, x2 ∈ \( \mathbb{E} \)1}. It is proved the infinite differentiability in ΩH of those generalized solutions of the equation P(D)u = 0, for which D2ju ∈ L2(ΩH), j = 0, …, ordx2P.