Results 1 to 10 of about 1,014 (85)

A Short Proof of H\"older Continuity for Functions in DeGiorgi Classes [PDF]

Annales Academi{\ae} Scientiarum Fennic{\ae} Mathematica, Volumen 43, 2018, 931-934, 2017
The goal of this note is to give an alternative proof of local H\"older continuity for functions in DeGiorgi classes based on an idea of Moser.Comment: 5 ...
Klaus, Colin, Liao, Naian
core   +2 more sources

Flat solutions of the 1-Laplacian equation [PDF]

, 2017
For every $f \in L^N(\Omega)$ defined in an open bounded subset $\Omega$ of $\mathbb{R}^N$, we prove that a solution $u \in W_0^{1, 1}(\Omega)$ of the $1$-Laplacian equation ${-}\mathrm{div}{(\frac{\nabla u}{|\nabla u|})} = f$ in $\Omega$ satisfies ...
Orsina, Luigi, Ponce, Augusto C.
core   +3 more sources

On Coron's problem for the p-Laplacian [PDF]

, 2014
We prove that the critical problem for the $p$-Laplacian operator admits a nontrivial solution in annular shaped domains with sufficiently small inner hole.
Mercuri, Carlo, Sciunzi, Berardino, Squassina, Marco   +2 more
core   +1 more source

An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes

, 2020
In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes.
Della Pietra, Francesco, Piscitelli, Gianpaolo   +1 more
core   +1 more source

A quasilinear problem with fast growing gradient

, 2012
In this paper we consider the following Dirichlet problem for the $p$-Laplacian in the positive parameters $\lambda$ and $\beta$: [{{array} [c]{rcll}% -\Delta_{p}u & = & \lambda h(x,u)+\beta f(x,u,\nabla u) & \text{in}\Omega u & = & 0 & \text{on}\partial\
Bueno, Hamilton, Ercole, Grey
core   +1 more source

A Note on why Enforcing Discrete Maximum Principles by a simple a Posteriori Cutoff is a Good Idea

, 2012
Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we enforce the discrete maximum principle by performing a simple cutoff.
Kreuzer, Christian
core   +1 more source

Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes

, 2020
We study, in dimension $n\geq2$, the eigenvalue problem and the torsional rigidity for the $p$-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions.
Paoli, Gloria, Piscitelli, Gianpaolo, Trani, Leonardo   +2 more
core   +1 more source

A remark on an overdetermined problem in Riemannian Geometry

, 2015
Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$
A Enciso, A Farina, A Greco, A Greco, AL Vogel, Alberto Farina, B Brandolini, C Babaoglu, D Gilbarg, E Benedetto Di, E Hopf, GM Lieberman, HF Weinberger, J Heinonen, J Serrin, JL Lewis, M Choulli, N Garofalo, P Pucci, P Tolksdorf, QM Wang   +20 more
core   +1 more source

Fractional differentiability for solutions of the inhomogenous $p$-Laplace system

, 2017
It is shown that if $p \ge 3$ and $u \in W^{1,p}(\Omega,\mathbb{R}^N)$ solves the inhomogenous $p$-Laplace system \[ \operatorname{div} (|\nabla u|^{p-2} \nabla u) = f, \qquad f \in W^{1,p'}(\Omega,\mathbb{R}^N), \] then locally the gradient $\nabla u ...
Miśkiewicz, Michał
core   +1 more source

Positive solutions for nonvariational Robin problems

, 2018
We study a nonlinear Robin problem driven by the $p$-Laplacian and with a reaction term depending on the gradient (the convection term). Using the theory of nonlinear operators of monotone-type and the asymptotic analysis of a suitable perturbation of ...
Papageorgiou, Nikolaos S., Repovš, Dušan D., Rădulescu, Vicenţiu D.   +2 more
core   +2 more sources