20-39 Vitali Vougalter, Vitaly Volpert

Solvability in the sense of sequences for some non Fredholm operators with drift and superdiffusion (133K, pdf) Apr 22, 20

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Abstract. We study the solvability of certain linear nonhomogeneous elliptic problems and prove that under some technical assumptions the convergence in L^2 of their right sides implies the existence and the convergence in H^1 of the solutions. The equations contain first order differential operators with or without Fredholm property, in particular the square root of the one dimensional negative Laplacian, 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 solutions.

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