Related papers: Global Lorentz estimates for nonlinear parabolic e…

Let $n \ge 2$ and $\Omega \subset \mathbb{R}^n$ be a bounded Lipschitz domain. In this article, we establish first-order global regularity estimates in the scale of BMO spaces on $\Omega$ for weak solutions to the second-order elliptic…

We obtain the global weighted $W^{1,p}$ estimates for weak solutions of nonlinear elliptic equations over Reifenberg flat domains. Where nonlinearity $A(x,z,\xi)$ is assumed to be local uniform continuous in $z$ and have small BMO semi-norm…

We consider a generalized steady Stokes system with discontinuous coefficients in a nonsmooth domain when the inhomogeneous term belongs to a weighted $L^q$ space for $2<q<\infty$. We prove the global weighted $L^q$-estimates for the…

We obtain a global weighted $L^p$ estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in a nonsmooth bounded domain. The coefficients are assumed to be merely measurable in one…

We study global regularity for solutions of quasilinear elliptic equations of the form $\div \A(x,u,\nabla u) = \div \F $ in rough domains $\Omega$ in $\R^n$ with nonhomogeneous Dirichlet boundary condition. The vector field $\A$ is assumed…

This paper provides a local and global Calder\'on-Zygmund type estimate of a weak solution to the parabolic double-phase system. The proof of local estimate is based on comparison estimates and the scaling invariant property of the…

Our goal in this article is to study the global Lorentz estimates for gradient of weak solutions to $p$-Laplace double obstacle problems involving the Schr\"odinger term: $-\Delta_p u + \mathbb{V}|u|^{p-2}u$ with bound constraints $\psi_1…

We prove Calder\'on-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particular, the right-hand side is presented by a sum of…

We study fully nonlinear parabolic equations in nondivergence form with oblique boundary conditions. An optimal and global Calder\'{o}n-Zygmund estimate is obtained by proving that the Hessian of the viscosity solution to the oblique…

We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$-fractional Laplacian type equations. In particular, we prove sharp Calder\'on-Zygmund type estimates of $u/d^s$ depending on the regularity…

We obtain a global fractional Calder\'on-Zygmund regularity theory for the fractional Poisson problem. More precisely, for $\Omega \subset \mathbb{R}^N$, $N \geq 2$, a bounded domain with boundary $\partial \Omega$ of class $C^2$, $s \in…

We obtain $L^q$-regularity estimates for weak solutions to $p$-Laplacian type equations of differential forms. In particular, we prove local Calder\'on-Zygmund type estimates for equations with discontinuous coefficients satisfying the…

Let $2 \le N\in\mathbb{N}$, $\Omega$ be a bounded open in $\mathbb{R}^{N}$, $T\in (0,\infty)$, $Q=\Omega\times (0,T)$, $u$ be a weak solution of parabolic equation $\displaystyle \frac{\partial u}{\partial t} -Lu= f$, where $L$ is an…

This work is concerned with global gradient bounds for a class of divergence-form degenerate elliptic systems with complex-valued coefficients. Notably, the leading coefficients are merely required to be sufficiently small in BMO, which is…

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…

In this paper, we study some regularity issues concerning the gradient of weak solutions of $u_t - {\rm div} \mathcal{A}(x,t,\nabla u) = g$, where $\mathcal{A}(x,t,\nabla u)$ is modeled after the $p$-Laplace operator. The main results we…

We deal with boundary value problems for second-order nonlinear elliptic equations in divergence form, which emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of…

This paper is a survey of some recent results on the validity and the failure of global $W^{2,p}$ regularity properties of smooth solutions of the Poisson equation $\Delta u = f$ on a complete Riemannian manifold $(M,g)$. We review…

This paper is a contribution to the study of regularity theory for nonlinear elliptic equations. The aim of this paper is to establish some global estimates for non-uniformly elliptic in divergence form as follows \begin{align*}…

We establish local Calder\'on-Zygmund type estimates for weak solutions to nonlinear parabolic systems with $p$-growth and VMO coefficients. In particular, we prove that if the right-hand side belongs locally to $L^{\mu s}$, where the…