Related papers: Global weighted gradient estimates for nonlinear p…

In this paper, we establish refined regularity estimates for nonnegative solutions to the fractional Poisson equation $$ (-\Delta)^s u(x) =f(x),\,\, x\in B_1(0). $$ Specifically, we have derived H\"{o}lder, Schauder, and Ln-Lipschitz…

In this paper, we study the regularity of weak solutions and subsolutions of second-order elliptic equations having a gradient term with superquadratic growth. We show that, under appropriate integrability conditions on the data, all weak…

In this paper, we study the global regularity estimates in Lorentz spaces for gradients of solutions to quasilinear elliptic equations with measure data of the form \begin{eqnarray*} \left\{ \begin{array}{rcl} -{\rm div}(\mathcal{A}(x,…

The focus of this paper is the study of the regularity properties of the time harmonic Maxwell's equations with anisotropic complex coefficients, in a bounded domain with $C^{1,1}$ boundary. We assume that at least one of the material…

We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique $W^{1,p}$ solvability is obtained with $p$ being in the optimal range $(4/3,4)$. The leading coefficients are assumed…

We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish…

We prove $L_p$ estimates of solutions to a conormal derivative problem for divergence form complex-valued higher-order elliptic systems on a half space and on a Reifenberg flat domain. The leading coefficients are assumed to be merely…

The aim of this paper is to develop the regularity theory for a weak solution to a class of quasilinear nonhomogeneous elliptic equations, whose prototype is the following mixed Dirichlet $p$-Laplace equation of type \begin{align*}…

The classical arguments employed when obtaining error estimates of Finite Element (FE) discretisations of elliptic problems lead to more restrictive assumptions on the regularity of the exact solution when applied to non-conforming methods.…

In this article, we reproduce results of classical regularity theory of quasilinear elliptic equations in the divergence form, in the setting of Heisenberg Group. The considered cases encompass a very wide class of equations with isotropic…

We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of a lower bound for the right-hand side function. This…

We prove that the fractional derivatives of solutions to a class of nonlocal fully nonlinear elliptic equations are epsilon-integrable. We follow Fanghua Lin's original approach to the analogous problem for second order equations, by first…

We study regularity for solutions of quasilinear elliptic equations of the form $\div \A(x,u,\nabla u) = \div \F $ in bounded domains in $\R^n$. The vector field $\A$ is assumed to be continuous in $u$, and its growth in $\nabla u$ is like…

We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale $L^\infty$-type estimate for the gradient of a solution. The estimate…

In this paper, we establish pointwise boundary ${{C}^{1,\alpha}}$ estimates for viscosity solutions of some degenerate fully nonlinear elliptic equations on ${C^{1,\alpha}}$ domains. Instead of straightening out the boundary, we utilize the…

We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-laplacian type, with $p$ in the sub-critical range $(1,\frac{2N}{N+1}]$. The…

In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates for gradients of solutions to the quasilinear parabolic equations: $$u_t-\operatorname{div}(A(x,t,\nabla u))=\operatorname{div}(F),$$ in a bounded domain…

We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial…

Let $\Omega\subset R^n$ be a bounded convex domain with $n\ge2$. Suppose that $A$ is uniformly elliptic and belongs to $W^{1,n}$ when $n\ge 3$ or $W^{1,q}$ for some $q>2$ when $n=2$. For $1<p<\infty$, we build up a global second order…

We give sharp $C^{2,\alpha}$ estimates for solutions of some fully nonlinear elliptic and parabolic equations in complex geometry and almost complex geometry, assuming a bound on the Laplacian of the solution. We also prove the analogous…