Solvability Relations For Some Diffusion Equations With Convection Terms - Vougalter, Vitali; Volpert, Vitaly (Discontinuity, Nonlinearity, and Complexity, 2026)
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 Rd. The corresponding operator L may be non Fredholm, such that solvability conditions for the equation Lu = f are unknown. We obtain solvability conditions in H2 (Rd ) for the non selfadjoint problem via relating it to a self-adjoint Schrödinger type operator, for which solvability relations are derived in our preceding work [16].