Smoothness of solutions of almost hypoelliptic equations
V. G. Karapetyan · Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) · 2009
The paper studies a class of almost hypoelliptic equations P(D)U = ƒ in a strip. It is proved that for $$ \mathcal{H} $$ great enough and for δ > 0 small enough all solutions of this equation, which are square summable with the weight e −δ|x| and for which $$ D_2^{\alpha _2 } U $$ , where α 2 = 0, …, $$ ord_{\alpha _2 } P $$ , are infinitely differentiable in x 1 functions, provided D 1 ƒ ∈ L 2( $$ \Omega _\mathcal{H} $$ ) for any j.