- 22-75 Vitali Vougalter
- Solvability in the sense of sequences for some non-Fredholm operators
with the drift and bi-Laplacian
(137K, pdf)
Nov 11, 22
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Abstract. We study the solvability of some linear nonhomogeneous elliptic equations
and establish that under certain technical conditions the convergence in
L^2 of their right sides yields the existence and the convergence in H^4
of the solutions. The problems involve the fourth order differential operators with or without the Fredholm property, particularly the fourth derivative operator, on the whole real line or on a finite interval with
periodic boundary conditions. We demonstrate that the transport term contained in these equations provides the regularization of the solutions.
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