Related papers: Global gradient bounds for the parabolic p-Laplaci…

We will prove a global estimate for the gradient of the solution to the {\it Poisson differential inequality} $|\Delta u(x)|\le a|\nabla u(x)|^2+b$, $x\in B^{n}$, where $a,b<\infty$ and $u|_{S^{n-1}}\in C^{1,\alpha}(S^{n-1}, \Bbb R^m)$. If…

We derive a priori bounds for positive supersolutions of $ - \Delta_{p} u = \rho(x) f(u) $, where $p>1$ and $\Delta_{p}$ is the $p$-Laplace operator, in a smooth bounded domain of $R^{N}$ with zero Dirichlet boundary conditions. We apply…

We establish interior and up to the boundary H\"older regularity estimates for weak solutions of the Dirichlet problem for the fractional $g-$Laplacian with bounded right hand side and $g$ convex. These are the first regularity results…

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 an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to degenerate parabolic equations of $p$-laplacian type. The estimate is given in terms of a Wiener-type integral,…

This paper investigates the initial-boundary value problem for a nonlinear parabolic equation involving the $p$-Laplacian operator, nonlocal source terms, gradient absorption, and various nonlinearities: \[ \frac{\partial u}{\partial t} -…

We prove sharp regularity estimates for solutions of highly degenerate fully nonlinear elliptic equations. These are free boundary models in which a nonlinear diffusion process drives the system only in the region where the gradient…

We consider the Dirichlet problem for positive solutions of the equation $-\Delta_p (u) = f(u)$ in a convex, bounded, smooth domain $\Omega \subset\R^N$, with $f$ locally Lipschitz continuous. \par We provide sufficient conditions…

We consider energy solutions of the inhomogeneous parabolic $p$-Laplacien system $\partial_t u-\text{div}(|D u|^{p-2}D u)=-\text{div} g$. We show in the case $p\geq 2$ that if the right hand side $g$ is locally in $L^\infty(\text{BMO})$,…

The global equi-continuity estimate on $L^p$-viscosity solutions of parabolic bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of $L^p$-viscosity solutions is…

In the theory of second-order, nonlinear elliptic and parabolic equations, obtaining local or global gradient bounds is often a key step for proving the existence of solutions but it may be even more useful in many applications, for example…

We present pointwise gradient bounds for solutions to $p$-Laplacean type non-homogeneous equations employing non-linear Wolff type potentials, and then prove similar bounds, via suitable caloric potentials, for solutions to parabolic…

We prove boundary H\"older and Lipschitz regularity for a class of degenerate elliptic, second order, inhomogeneous equations in non-divergence form structured on the left-invariant vector fields of the Heisenberg group. Our focus is on the…

In this article, we focus on a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional $p$-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in $\mathbb{R}^{d}$ and composed…

We establish the solvability of the $L^p$-Dirichlet and $L^{p^\prime}$-Neumann problems for the Laplacian for $p\in (\frac{n}{n-1}-\varepsilon,\frac{2n}{n-1}]$ for some $\varepsilon>0$ in $2$-sided chord-arc domains with unbounded boundary…

In the paper, we prove the existence of radial solutions to \begin{equation}\notag%\label{main-eq-abstarct} %\begin{aligned} -\Delta_p u+({\rm sgn}(p-s)+V(x))|u|^{p-2}u+\lambda |u|^{s-2}u=|u|^{q-2}u\qquad\text{in}\,\R^N \\…

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…

We establish global H\"older regularity for eigenfunctions of the fractional $g-$Laplacian with Dirichlet boundary conditions where $g=G'$ and $G$ is a Young functions satisfying the so called $\Delta_2$ condition. Our results apply to more…

In this paper we prove local interior and boundary Lipschitz continuity of solutions of a free boundary problem involving the $A$-Laplacian. We also show that the free boundary is represented locally by graphs of a family of lower…

Let $n\ge2$ and $\Omega$ be a bounded Lipschitz domain in $\mathbb{R}^n$. In this article, the authors investigate global (weighted) estimates for the gradient of solutions to Robin boundary value problems of second order elliptic equations…