Related papers: Boundary Harnack principle on uniform domains

We establish boundary estimates for non-negative solutions to the p-parabolic equation in the degenerate range $p>2$. Our main results include new parabolic intrinsic Harnack chains in cylindrical NTA-domains together with sharp boundary…

We prove continuity and Harnack's inequality for bounded solutions to elliptic equations of the type $$ \begin{aligned} {\rm div}\big(|\nabla u|^{p-2}\,\nabla u+a(x)|\nabla u|^{q-2}\,\nabla u\big)=0,& \quad a(x)\geqslant0, \\…

We prove forward and backward parabolic boundary Harnack principles for nonnegative solutions of the heat equation in the complements of thin parabolic Lipschitz sets given as subgraphs $E=\{(x,t): x_{n-1}\leq f(x'',t),x_n=0\}\subset…

In this article we prove for the first time the $C^s$ boundary regularity for solutions to nonlocal elliptic equations with H\"older continuous coefficients in divergence form in $C^{1,\alpha}$ domains. So far, it was only known that…

In this paper, we consider a weakly coupled system of nonlocal operators which contain both diffusion part with uniformly elliptic diffusion matrices and bounded drift vectors and the jump part with relatively general jump kernels. We use…

Let $(X,\mathcal W)$ be a balayage space, $1\in \mathcal W$, or - equivalently - let $\mathcal W$ be the set of excessive functions of a Hunt process on a locally compact space $X$ with countable base such that $\mathcal W$ separates…

We provide a higher order boundary Harnack inequality for harmonic functions in slit domains. As a corollary we obtain the $C^\infty$ regularity of the free boundary in the Signorini problem near non-degenerate points.

We prove the Harnack inequality for antisymmetric $s$-harmonic functions, and more generally for solutions of fractional equations with zero-th order terms, in a general domain. This may be used in conjunction with the method of moving…

We study local regularity properties for solutions of linear, non-uniformly elliptic equations. Assuming certain integrability conditions on the coefficient field, we prove local boundedness and Harnack inequality. The assumed integrability…

We prove that the elliptic Harnack inequality (on a manifold, graph, or suitably regular metric measure space) is stable under bounded perturbations, as well as rough isometries.

This paper is concerned with nonlinear elliptic equations in nondivergence form where the operator has a first order drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative…

In this note, we prove the boundary H\"{o}lder regularity for the infinity Laplace equation under a proper geometric condition. This geometric condition is quite general, and the exterior cone condition, the Reifenberg flat domains, and the…

We study boundary conditions for elliptic operators on non-compact manifolds with boundary via uniform K-homology, a version of K-homology sensitive to the large-scale geometry of the manifold. To that end, we develop the theory of relative…

Under the lack of variational structure and nondegeneracy, we investigate three notions of \textit{generalized principal eigenvalue} for a general infinity Laplacian operator with gradient and homogeneous term. A Harnack inequality and…

We obtain a global extension of the classical weak Harnack inequality which extends and quantifies the Hopf-Oleinik boundary-point lemma, for uniformly elliptic equations in divergence form. Among the consequences is a boundary gradient…

We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a…

We consider the singular boundary-value problem \Delta u = f(u) in D; u|_dD= phi, where 1. D is a bounded C^2-domain of R^d, d >= 3 2. f: (0,1) -> (0,1) is a locally H\"older continuous function such that f(u) -> 1 as u -> 0 at the rate…

We prove new boundary Harnack inequalities in Lipschitz domains for equations with a right hand side. Our main result applies to non-divergence form operators with bounded measurable coefficients and to divergence form operators with…

Graham Theorem on the unit ball $B_{n}$ in $\mathbb{C}^{n}$ states that every invariant harmonic function $u\in C^{n}(\overline{B}_{n})$ must be pluriharmonic in $B_{n}$. This rigidity phenomenon of Graham have been studied by many authors.…

The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator…