Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Meyers type regularity result for approximations of second order elliptic operators by Galerkin schemes
127
0
0.0
(
0
)
Authors
Nadine Badr
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 second order ordinary differential operators with polynomial coefficients and symbol of degree $2$. This correspondence is established by a transformation of Wigner type. In this way the global regularity of twisted partial differential operators turns out to be equivalent to global regularity and injectivity of the corresponding ordinary differential operators, which can be completely characterized in terms of the asymptotic behavior of the Weyl symbol. In conclusion we observe that we have obtained a new class of globally regular partial differential operators which is disjoint from the class of hypo-elliptic operators in the sense of Shubin.
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 then prove the Schauder estimates for solutions if the equation is convex.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
