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We prove a Meyers type regularity estimate for approximate solutions of second order elliptic equations obtained by Galerkin methods. The proofs rely on interpolation results for Sobolev spaces on graphs. Estimates for second order elliptic operators on rather general graphs are also obtained.
In this paper we characterize global regularity in the sense of Shubin of twisted partial differential operators of second order in dimension $2$. These operators form a class containing the twisted Laplacian, and in bi-unique correspondence with sec
This paper is concerned with higher Holder regularity for viscosity solutions to non-translation invariant second order integro-PDEs, compared to cite{mou2018}. We first obtain $C^{1,alpha}$ regularity estimates for fully nonlinear integro-PDEs. We t
We consider nonlinear fourth order elliptic equations of double divergence type. We show that for a certain class of equations where the nonlinearity is in the Hessian, solutions that are C^{2,alpha} enjoy interior estimates on all derivatives.
We review recent progress in potential theory of second-order elliptic operators and on the metastable behavior of Markov processes.
In this paper, we obtain a uniform $W^{2,varepsilon}$-estimate of solutions to the fully nonlinear uniformly elliptic equations on Riemannian manifolds with a lower bound of sectional curvature using the ABP method.