Results 31 to 40 of about 561 (74)
Gradient and Lipschitz estimates for tug-of-war type games
, 2020 We define a random step size tug-of-war game, and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p ...
Attouchi, Amal +2 more
core +1 more source
On the problem of unique continuation for the p-Laplace equation
, 2014 We study if two different solutions of the $p$-Laplace equation $$\nabla\cdot(|\nabla u|^{p-2}\nabla u)=0,$$ where ...
Alessandrini +21 more
core +1 more source
Stability of eigenvalues for variable exponent problems
, 2015 In the framework of variable exponent Sobolev spaces, we prove that the variational eigenvalues defined by inf sup procedures of Rayleigh ratios for the Luxemburg norms are all stable under uniform convergence of the exponents.Comment: 10 ...
Colasuonno, Francesca, Squassina, Marco
core +1 more source
Singular quasilinear elliptic systems in $\mathbb{R}^N$
, 2018 The existence of positive weak solutions to a singular quasilinear elliptic system in the whole space is established via suitable a priori estimates and Schauder's fixed point ...
Marano, S. A., Marino, G., Moussaoui, A.
core +1 more source
Advanced Nonlinear StudiesIn this note, we obtain a classification result for positive solutions to the critical p-Laplace equation in Rn ${\mathbb{R}}^{n}$ with n ≥ 4 and p > p n for some number pn∈n3,n+13 ${p}_{n}\in \left(\frac{n}{3},\frac{n+1}{3}\right)$ such that pn∼n3+1n $
Vétois Jérôme
doaj +1 more source
Some remarks on sign changing solutions of a quasilinear elliptic equation in two variables [PDF]
, 2012 We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions; the boundary data is assumed to have finite number of relative maximum and minimum values.
Granlund, Seppo, Marola, Niko
core
A-priori bounds for quasilinear problems in critical dimension
Advances in Nonlinear Analysis, 2019 We establish uniform a-priori bounds for solutions of the quasilinear ...
Romani Giulio
doaj +1 more source
Existence results for double-phase problems via Morse theory
, 2016 We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups at zero.Comment: 11 ...
Perera, Kanishka, Squassina, Marco
core +1 more source
Harnack inequality for a class of functionals with non-standard growth via De Giorgi’s method
Advances in Nonlinear Analysis, 2018 We study the regularity theory of quasi-minimizers of functionals with Lp(⋅)logL{L^{p(\,\cdot\,)}\log L}-growth. In particular, we prove the Harnack inequality and, in addition, the local boundedness and the Hölder continuity of the quasi-minimizers ...
Ok Jihoon
doaj +1 more source
Normalized solutions for the double-phase problem with nonlocal reaction
Advances in Nonlinear AnalysisIn this article, we consider the double-phase problem with nonlocal reaction. For the autonomous case, we introduce the methods of the Pohozaev manifold, Hardy-Littlewood Sobolev subcritical approximation, adding the mass term to prove the existence and ...
Cai Li, Zhang Fubao
doaj +1 more source