Smoothness of solutions of almost hypoelliptic equations |
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| Authors: | V G Karapetyan |
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| Institution: | (1) Yerevan State University, Yerevan, Armenia |
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| Abstract: | The paper studies a class of almost hypoelliptic equations P(D)U = ? 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 j ? ∈ L 2(\(\Omega _\mathcal{H} \)) for any j. |
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| Keywords: | Hypoelliptic almost hypoelliptic embedding theorem regularity of solutions |
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