Related papers: The Optimal H\"older Exponent in Massari's Regular…

We consider a class of nonlinear integro-differential equations whose leading operator is obtained as a superposition of $(-\Delta_{p})^{s}$ and $(-\Delta_{p})^{t}$, where $0<s<t<1<p<\infty$, weighted via two possibly degenerate…

We characterise equality cases in matrix H\"older's inequality and develop a divergence formulation of optimal transport of vector measures. As an application, we reprove the representation formula for measures in the polar cone to monotone…

We obtain sharp bounds for the modulus of continuity of the uncentered maximal function in terms of the modulus of continuity of the given function, via integral formulas. Some of the results deduced from these formulas are the following:…

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…

We prove two H\"older regularity results for solutions of generated Jacobian equations. First, that under the A3 condition and the assumption of nonnegative $L^p$ valued data solutions are $C^{1,\alpha}$ for an $\alpha$ that is sharp. Then,…

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…

Let L be a Schr\"odinger operator of the form L=-\Delta+V, where the nonnegative potential V satisfies a reverse H\"older inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted H\"older…

This paper deals with $(K_1, K_2)$-quasiregular mappings. It is shown, by Morrey's Lemma and isoperimetric inequality, that every $(K_1, K_2)$-quasiregular mapping satisfies a H\"older condition with exponent $\alpha$ on compact subsets of…

This paper develops a quantitative regularity theory for the Lyapunov exponents of random products of matrices in $\operatorname{GL}(2,\mathbb{R})$, with extensions to $\operatorname{GL}(d,\mathbb{R})$ for all $d \geq 2$. At every compactly…

We consider a Kantorovich potential associated to an optimal transportation problem between measures that are not necessarily absolutely continuous with respect to the Lebesgue measure, but are comparable to the Lebesgue measure when…

The aim of this paper is to establish regularity for weak solutions to the nondiagonal quasilinear degenerate elliptic systems related to H\"{o}rmander's vector fields, where the coefficients are bounded with vanishing mean oscillation. We…

We consider Lipschitz and H\"{o}lder continuous random dynamical systems defined by a distribution with a finite logarithmic moment. We prove that under suitable non-degeneracy conditions every stationary measure must be $\log$-H\"{o}lder…

We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally H\"older continuous with H\"older exponent depending only on the…

Regularity and singularity of the solutions according to the shape of domains is a challenging research theme in the Boltzmann theory (\cite{Kim11,GKTT1}). In this paper, we prove an H\"older regularity in $C^{0,\frac{1}{2}-}_{x,v}$ for the…

The links between the mean families of Lehmer and H\"older and the weighted maximum likelihood estimator have recently been established in the case of a regular univariate exponential family. In this article, we will extend the outcomes…

We consider the maximal regularity problem for non-autonomous evolution equations \begin{equation} \left\{ \begin{array}{rcl} u'(t) + A(t)\,u(t) &=& f(t), \ t \in (0, \tau] u(0)&=&u_0. \end{array} \right. \end{equation} Each operator $A(t)$…

This paper considers a class of nonlinear, degenerate drift- diffusion equations. We study well-posedness and regularity properties of the solutions, with the goal to achieve uniform H\"{o}lder regularity in terms of $L^p$-bound on the…

In this paper we study maximal $L^p$-regularity for evolution equations with time-dependent operators $A$. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the…

We introduce the Lebesgue--H\"{o}lder--Dini and Lebesgue--H\"{o}lder spaces $L^p(\mathbb{R};{\mathcal C}_{\vartheta,\varsigma}^{\alpha,\rho}({\mathbb R}^n))$ ($\vartheta\in \{l,b\}, \, \varsigma\in \{d,s,c,w\}$, $p\in (1,+\infty]$ and…

We study the problem of optimizing the eigenvalues of the Dirichlet Laplace operator under perimeter constraint. We prove that optimal sets are analytic outside a closed singular set of dimension at most $d-8$ by writing a general…