On the smoothness of solutions of a class of regular equations in a strip |
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| Authors: | S R Hayrapetyan |
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| Institution: | 1.Russian-Armenian (Slavonic) State University,Yerevan,Armenia |
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| Abstract: | The paper considers a class of regular, hypoelliptic in x
1, two-dimensional operators P(D) = P(D
1,D
2) in rather wide strip Ω
H
= {x = (x
1; x
2) ∈ $
\mathbb{E}
$
\mathbb{E}
2, |x
1| < H, x
2 ∈ $
\mathbb{E}
$
\mathbb{E}
1}. It is proved the infinite differentiability in Ω
H
of those generalized solutions of the equation P(D)
u
= 0, for which D
2
j
u ∈ L
2(Ω
H
), j = 0, …, ord
x2
P. |
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| Keywords: | |
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