Vitali Vougalter, Vitaly Volpert
Solvability relations for some diffusion equations with convection terms
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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.