Related papers: Higher order H{\"o}lder approximation by solutions…

We establish that a generalized H\"{o}lder continuous function on an $(m-2)$-Ahlfors regular compact set in $\mathbb{R}^m$ can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity…

We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform H\"older-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form $-\nabla…

We prove the existence of globally H\"{o}lder continuous solutions to certain elliptic partial differential equations with lower-order terms. Our result is applicable to coefficients controlled by a negative power of the distance from the…

Let $(\mathbb{X} , d, \mu )$ be a proper metric measure space and let $\Omega \subset \mathbb{X}$ be a bounded domain. For each $x\in \Omega$, we choose a radius $0< \varrho (x) \leq \mathrm{dist}(x, \partial \Omega ) $ and let $B_x$ be the…

We show that bounded solutions of the quasilinear elliptic equation $\Delta_{p(x)} u=g+div(\textbf{F})$ are locally H\"{o}lder continuous provided that the functions $g$ and $\textbf{F}$ are in suitable Lebesgue spaces.

In this article, we improve the convergence order of some finite volume solutions approximating some second order elliptic problems. We prove that finite volume approximations of order $O(h^{k+1})$, with $k$ integer, can be obtained after…

Given a Hilbert space $\mathcal H$ and a finite measure space $\Omega$, the approximation of a vector-valued function $f: \Omega \to \mathcal H$ by a $k$-dimensional subspace $\mathcal U \subset \mathcal H$ plays an important role in…

We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type $\ddot u(s) + 2 B \dot u(s) + A u(s) = f(s) (\ast),$ where $A, B$ are densely defined closed linear operators acting in a…

This paper aims to establish the existence of a weak solution for the non-local problem: \begin{equation*} \left\{\begin{array}{ll} -a\left(\int_{\Omega}\mathcal{H}(x,|\nabla u|)dx \right) \Delta_{\mathcal{H}}u &=f(x,u) \ \ \hbox{in} \ \…

We consider the question of whether the high-energy eigenfunctions of certain Schr\"odinger operators on the $d$-dimensional hyperbolic space of constant curvature $-\kappa^2$ are flexible enough to approximate an arbitrary solution of the…

We study the local H\"older regularity of strong solutions $u$ of second-order uniformly elliptic equations having a gradient term with superquadratic growth $\gamma > 2$, and right-hand side in a Lebesgue space $L^q$. When $q >…

In this article, we will consider second order uniformly elliptic operators of divergence form defined on R^n with measurable coefficients. Mainly, we will give estimates on the dimension of space of solutions that grow at most polynomially…

In this paper, we examine the regularity of the solutions to the double-divergence equation. We establish improved H\"older continuity as solutions approach their zero level-sets. In fact, we prove that $\alpha$-H\"older continuous…

We identify a large class of constant (complex) coefficient, second order elliptic systems for which the Dirichlet problem in the upper-half space with data in $L^p$-based Sobolev spaces, $1<p<\infty$, of arbitrary smoothness $\ell$, is…

This work is about global H\"older regularity for solutions to elliptic partial differential equations subject to mixed boundary conditions on irregular domains. There are two main results. In the first, we show that if the domain of the…

For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the…

In this paper, we study the positive solutions to the following singular and non local elliptic problem posed in a bounded and smooth domain $\Omega\subset \R^N$, $N> 2s$: % \begin{eqnarray*} (P_\lambda)\left\{\begin{array}{lll}…

Second-order two-scale expansions, a unified proof for the regularity of the correctors based on the translation invariant and a lemma for extracting $O(\epsilon)$ from the remainder term are presented for the second order nonlinear…

Aim of this paper is to prove the second order differentiation formula for $H^{2,2}$ functions along geodesics in $RCD^*(K,N)$ spaces with $N < \infty$. This formula is new even in the context of Alexandrov spaces, where second order…

We prove well-posedness results for the Dirichlet problem in $\mathbb{R}^{n}_{+}$ for homogeneous, second order, constant complex coefficient elliptic systems with boundary data in generalized H\"older spaces…