Related papers: Generalized Evans--Krylov and Schauder type estima…
In this paper, we consider fully nonlinear integro-differential equations with possibly nonsymmetric kernels. We are able to find different versions of Alexandroff-Backelman-Pucci estimate corresponding to the full class $\cS^{\fL_0}$ of…
Under various conditions, we establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the…
In this paper, we examine regularity estimates for solutions to fully nonlinear, degenerated elliptic equations, at interior vanishing source points. At these points, we obtain Schauder-type regularity estimates, which depend on the…
In this work we provide an Aleksandrov-Bakelman-Pucci type estimate for a certain class of fully nonlinear elliptic integro-differential equations, the proof of which relies on an appropriate generalization of the convex envelope to a…
We show interior Schauder estimates for a special class of fully nonlinear parabolic Isaacs equations by the maximum principle, providing an Evans-Krylov result for the model equation $\min\{\inf_{\beta}L_\beta u,\sup_\gamma L_\gamma…
In this work, we establish higher-order div-curl type estimates in the sense of Coifman, Lions, Meyer & Semmes, in a local setting for elliptic homogeneous linear differential operators with smooth coefficients acting on localizable Hardy…
We consider higher order linear, uniformly elliptic equations with non-smooth coefficients in Banach-Sobolev spaces generated by weighted general Banach Function Space (BFS). Supposing boundedness of the Hardy-Littlewood Maximal and…
We establish a Schauder-type estimate for general local and non-local linear parabolic system $$\partial_tu+\mathbf{L}_su=\Lambda^\gamma f+g$$ in $(0,\infty)\times\mathbb{R}^d$ where $\Lambda=(-\Delta)^{\frac{1}{2}}$, $0<\gamma\leq s$,…
We study singular integral operators with variable Calder\'on--Zygmund kernels and their commutators with $VMO$ functions in the framework of Orlicz spaces. After revisiting the classical $L^p$ theory, we establish boundedness results in…
We establish H\"older and Harnack estimates for weak solutions of a class of elliptic nonlocal equations that are modeled on integro-differential operators with kernels of measure. The approach is of De Giorgi-type, as developed by…
We obtain an asymptotic H\"older estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized…
We consider a class of noncooperative Schr\"{o}dinger-Kirchhoff type system which involves a general variable exponent elliptic operator with critical growth. Under certain suitable conditions on the nonlinearities, we establish the…
Schauder Orlicz-type estimates are derived for weak solutions to second-order linear elliptic equations in divergence form with lower-order terms. The Orlicz setting $X=L^\psi$ is treated first. Under suitable assumptions on the Young…
In this manuscript, we derive Schauder estimates for viscosity solutions to non-convex fully nonlinear second-order parabolic equations \[ \partial_t u - F(x, t,D^2u) = f (x, t) \quad \text{in} \quad \mathrm{Q}_1 = B_1 \times (-1, 0], \]…
We study robust regularity estimates for a class of nonlinear integro-differential operators with anisotropic and singular kernels. In this paper, we prove a Sobolev-type inequality, a weak Harnack inequality, and a local H\"older estimate.
We study the higher H\"older regularity of local weak solutions to a class of nonlinear nonlocal elliptic equations with kernels that satisfy a mild continuity assumption. An interesting feature of our main result is that the obtained…
We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of…
We establish global Schauder estimates for integro-partial differential equations (IPDE) driven by a possibly degenerate L\'evy Ornstein-Uhlenbeck operator, both in the elliptic and parabolic setting, using some suitable anisotropic…
In this note, motivated by our work on integral fully nonlinear equations, we provide a variation of the proof of Evans-Krylov theorem about the interior $C^{2,\alpha}$ a priori estimate for concave fully nonlinear elliptic equations. The…
In this paper we develop a new method based on Littlewood-Paley's decomposition and heat kernel estimates of integral form, to establish Schauder's estimate for the following degenerate nonlocal equation in $\mathbb R^{2d}$ with H\"older…