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

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.