Related papers: Improved H\"older regularity of fractional $(p,q)$…

We prove the local gradient H\"older regularity of viscosity solutions to the inhomogeneous normalized $p(x)$-Laplace equation $$ -\Delta u-(p(x)-2)\frac{\left\langle D^{2}uDu,Du\right\rangle }{\left|Du\right|^{2}} = f(x), $$ where $p$ is…

We prove H\"older estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$ \text{PV}…

In this article, we study nonlinear nonlocal equations with coercive gradient nonlinearity of the form \[ (-\Delta_p)^s u(x) + H(x, \nabla u) = f, \] where $f$ is Lipschitz continuous. We show that any viscosity solution $u$ is locally…

This paper is devoted to investigating the interior $C^{1, \alpha}$ regularity of viscosity solutions to the nonlocal double phase equations $$ \int_{\mathbb{R}^d}…

We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the $p$-Laplacian type and in non-divergence form. We provide local H\"older and Lipschitz estimates for the solutions. In the degenerate…

We show the existence of H\"older continuous periodic solution with compact support in time of the Boussinesq equations with partial viscosity. The H\"older regularity of the solution we constructed is anisotropic which is compatible with…

We establish regularity results for viscosity solutions to a class of quasilinear parabolic equations exhibiting nonhomogeneous degeneracy or singularity (a double phase regime) of the form \[ u_t - \big(|Du|^{\mathfrak{p}} +…

In this article, we investigate the H\"{o}lder regularity of the fractional $p$-Laplace equation of the form $(-\Delta_p)^s u=f$ where $p>1, s\in (0, 1)$ and $f\in L^\infty_{\rm loc}(\Omega)$. Specifically, we prove that $u\in C^{0,…

We prove some regularity estimates for viscosity solutions to a class of possible degenerate and singular integro-differential equations whose leading operator switches between two different types of fractional elliptic phases, according to…

In this paper we prove the H\"older regularity of bounded, uniformly continuous, viscosity solutions of some degenerate fully nonlinear equations in the Heisenberg group.

In this paper, we obtain gradient continuity estimates for viscosity solutions of $\Delta_{p}^N u= f$ in terms of the scaling critical $L(n,1 )$ norm of $f$, where $\Delta_{p}^N$ is the normalized $p-$Laplacian operator defined in (1.2)…

We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of…

In this article, we communicate with the glimpse of the proofs of global regularity results for weak solutions to a class of problems involving fractional $(p,q)$-Laplacian, denoted by $(-\Delta)^{s_1}_{p}+(-\Delta)^{s_2}_{q}$, for $s_2,…

We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of…

In this paper, we use local fraction derivative to show the H\"older continuity of the solution to the following nonlinear time-fractional slow and fast diffusion equation:…

We study the fractional $(p,q)$-Laplace equation $$ (-\Delta_p)^s u +(-\Delta_q)^t u= 0 $$ for $s,t\in(0,1)$ and $p,q\in(1,\infty)$. We establish H\"older estimates with an explicit exponent. As a consequence, we derive a Liouville-type…

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,…

In this paper we consider viscosity solutions of a class of non-homogeneous singular parabolic equations $$\partial_t u-|Du|^\gamma\Delta_p^N u=f,$$ where $-1<\gamma<0$, $1<p<\infty$, and $f$ is a given bounded function. We establish…

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…

This paper proves H\"older continuity of viscosity solutions to certain nonlocal parabolic equations that involve a generalized fractional time derivative of Marchaud or Caputo type. As a necessary and preliminary result, this paper first…