Regularity of nonlinear diffusion flows on noncompact manifolds, symmetries of variations and coercitivity condition in this case

Abstract:
In this talk we discuss the conditions on  any order regularity of nonlinear diffusion flows on noncompact Riemannian manifolds. Our approach is based on the use of high order symmetries of variational equations and a set of a priori nonlinear estimates on their solutions. The corresponding conditions on regularity generalize the classical assumptions of dissipativity and coercitivity to the case of manifold.