Related papers: Improved H\"older regularity for strongly elliptic…

In this paper, we obtain an improved H\"older regularity for quasiregular gradient mappings which was studied by Baernstein and Kovalev.

We establish sharp local $C^{1,\alpha}$-regularity for weak solutions to degenerate elliptic equations of $p$-Laplacian type with data in Morrey spaces. The proof relies on the Fefferman-Phong inequality and standard tools from regularity…

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 estimate the Hoelder exponent $\alpha$ of solutions to the Beltrami equation $\dbar f=\mu\de f$, where the Beltrami coefficient satisfies $\|\mu\|_\infty<1$. Our estimate improves the classical estimate $\alpha\ge\|K_\mu\|^{-1}$, where…

We present a general blow-up technique to obtain local regularity estimates for solutions, and their derivatives, of second order elliptic equations in divergence form in H\"older spaces with variable exponent. The procedure allows to…

This paper is concerned with higher H\"older regularity for viscosity solutions to non-translation invariant second order integro-PDEs, compared to \cite{mou2018}. We first obtain $C^{1,\alpha}$ regularity estimates for fully nonlinear…

This article concerns the results obtained in [Cabr\'e, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)], which established the H\"older regularity of stable solutions to semilinear elliptic equations in the optimal range of dimensions…

We prove maximal Schauder regularity for solutions to elliptic systems and Cauchy problems, in the space $C_b(\mathbb{R}^d;\mathbb{R}^m)$ of bounded and continuous functions, associated to a class of nonautonomous weakly coupled…

We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…

We prove H\"older regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also…

We obtain an explicit H\"older regularity result for viscosity solutions of a class of second order fully nonlinear equations leaded by operator that are neither convex/concave nor uniformly elliptic.

We establish a general theorem improving regularity of solutions of elliptic pseudodifferential equations. It allows to resolve in a unified way the regularity issue for a broad class of nonlinear elliptic equations and systems appearing in…

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…

Extending the results of Nardi (2015), this note establishes an existence and uniqueness result for second-order uniformly elliptic PDEs in divergence form with Neumann boundary conditions. A Schauder estimate is also derived.

We provide estimates for the H\"older exponent of solutions to the Beltrami equation $\dbar f=\mu\de f+\nu\bar{\de f}$, where the Beltrami coefficients $\mu,\nu$ satisfy $\||\mu|+|\nu|\|_\infty<1$ and $\Im(\nu)=0$. Our estimates depend on…

We investigate the regularity of semi-stable, radially symmetric, and decreasing solutions for a class of quasilinear reaction-diffusion equations in the inhomogeneous context of Riemannian manifolds. We prove uniform boundedness, Lebesgue…

This paper is concerned with H\"older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain,…

We prove local H\"older continuity for non negative, locally bounded, local weak solutions to the class of doubly nonlinear parabolic equations $\partial_t (u_q) - \text{div} (|Du|^{p-2} Du) = 0$ for $p > 2$, $ 0 < q < p-1$. The proof…

In this paper, we are concerned with the H\"older regularity for solutions of the nonlocal evolutionary equation $$ \partial_t u+(-\Delta_p)^s u = 0. $$ Here, $(-\Delta_p)^s$ is the fractional $p$-Laplacian, $0<s<1$ and $1<p<2$. We…

We prove a surprising higher regularity for solutions to the nonlinear elliptic autonomous Beltrami equation in a planar domain $\Omega$, \[ f_\zbar = {\cal A}(f_z) \hskip15pt a.e.\;\; z\in \Omega, \] when ${\cal A}$ is linear at $\infty$.…