Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds

Abstract In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented Neumann boundary conditions, when source term equation belongs a Lebesgue space, under various integrability regimes. Our method is based an integral refinement Bochner identity, and leads “semilinear Calderón–Zygmund” type results. Applications problem smoothness Mean Field Games systems conditions posed convex domains Euclidean space will also be discussed.