Solvability in the sense of sequences for some non Fredholm operators related to the superdiffusion

Vitali Vougalter (1) , Vitaly Volpert (2, 3, 4)

1 Department of Mathematics [University of Toronto]
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
3 ICJ - Institut Camille Jordan
4 MMCS - Modélisation mathématique, calcul scientifique

We study solvability of some linear nonhomogeneous elliptic equations and show that under reasonable technical conditions the convergence in L 2 (R d) of their right sides yields the existence and the convergence in H 1 (R d) of the solutions. The problems involve the square roots of the second order non Fredholm differential operators and we use the methods of spectral and scattering theory for Schrödinger type operators similarly to our preceding work [28].

Mots clés: Sobolev spaces; non Fredholm operators; solvability conditions

Domaines: Equations aux dérivées partielles [math.AP]

Vitali Vougalter, Vitaly Volpert. Solvability in the sense of sequences for some non Fredholm operators related to the superdiffusion. Journal of Pseudo-Differential Operators and Applications, 2017, 160, pp.1-22. ⟨10.1007/s11868-017-0204-1⟩. ⟨hal-01573772⟩