23-82 Vitali Vougalter

Solvability in the sense of sequences for some non-Fredholm operators with a drift and the cubed Laplacian (198K, pdf) Nov 25, 23

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Abstract. We study the solvability of certain linear nonhomogeneous elliptic problems and demonstrate that under the given technical assumptions the convergence in L^2 of their right-hand sides implies the existence and the convergence in H^6 of the solutions. The equations contain the sixth order differential operators with or without the Fredholm property, particularly the sixth derivative operator, on the whole real line or on a finite interval with periodic boundary conditions. We establish that the drift term involved in these problems provides the regularization of the solutions.

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