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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