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Vitali Vougalter, Vitaly Volpert
Solvability relations for some diffusion equations with convection terms
ABSTRACT. Linear second order elliptic equations containing the sum of the two Laplace operators with convection terms or a free Laplacian and a Laplacian with drift are considered in R^d. The corresponding operator L
may be non Fredholm, such that solvability conditions for the equation
Lu=f are unknown. We obtain solvability conditions in H^2(R^d) for the non self-adjoint problem via relating it to a self-adjoint Schroedinger
type operator, for which solvability relations are derived in our preceding work.