Results 1 to 10 of about 43,034 (224)
Tug-of-war and the infinity Laplacian [PDF]
Journal of the American Mathematical Society, 2008 We prove that every bounded Lipschitz function F on a subset Y of a length space X admits a tautest extension to X, i.e., a unique Lipschitz extension u for which Lip_U u = Lip_{boundary of U} u for all open subsets U of X that do not intersect Y. This
B. Wilson +4 more
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Discontinuous gradient constraints and the infinity Laplacian [PDF]
International Mathematics Research Notices, 2012 Motivated by tug-of-war games and asymptotic analysis of certain variational problems, we consider a gradient constraint problem involving the infinity Laplace operator.
D. Rossi +3 more
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The obstacle problem for the infinity fractional laplacian [PDF]
Rendiconti del Circolo Matematico di Palermo Series 2, 2016 Given g an α-H¨older continuous function defined on the boundary of a bounded domain Ω and given ψ a continuous obstacle defined in Ω, in this article, we find u an α-H¨older extension of g in Ω with u ≥ ψ.
Moreno Mérida, Lourdes +1 more
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Existence of solutions to a normalized F-infinity Laplacian equation
Electronic Journal of Differential Equations, 2014 In this article, for a continuous function F that is twice differentiable at a point $x_0$, we define the normalized F-infinity Laplacian $\Delta_{F; \infty}^N$ which is a generalization of the usual normalized infinity Laplacian. Then for a bounded
Hua Wang, Yijun He
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A Hölder infinity Laplacian obtained as limit of Orlicz fractional Laplacians [PDF]
Revista Matemática Complutense, 2021 This paper concerns with the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differential operators includes the fractional $p_n$-Laplacian when $p_n\to\infty$ as a particular case, tough it could be extended to a function ...
Fernandez Bonder, Julian +2 more
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Radial symmetry for a generalized nonlinear fractional p-Laplacian problem
Nonlinear Analysis, 2021 This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p ...
Wenwen Hou +3 more
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Reaction–diffusion equations for the infinity Laplacian [PDF]
Nonlinear Analysis, 2020 We derive sharp regularity for viscosity solutions of an inhomogeneous infinity Laplace equation across the free boundary, when the right hand side does not change sign and satisfies a certain growth condition. We prove geometric regularity estimates for solutions and conclude that once the source term is comparable to a homogeneous function, then the ...
Diehl, Nicolau M.L. +1 more
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The Gelfand problem for the Infinity Laplacian
Mathematics in Engineering, 2022 <abstract><p>We study the asymptotic behavior as $ p\to\infty $ of the Gelfand problem</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \left\{ \begin{aligned} -&\Delta_{p} u = \lambda\,e^{u}&& \text{in}\ \Omega\subset \mathbb{R}^n\\ &u = 0 ...
Fernando Charro +2 more
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A Hölder infinity Laplacian [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2011 In this paper we study the limit as p → ∞ of minimizers of the fractional W s,p -norms. In particular, we prove that the limit satisfies a non-local and non-linear equation. We also prove the existence and uniqueness of solutions of the equation.
Antonin Chambolle +2 more
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Evolution driven by the infinity fractional Laplacian
Calculus of Variations and Partial Differential Equations, 2023 AbstractWe consider the evolution problem associated to the infinity fractional Laplacian introduced by Bjorland et al. (Adv Math 230(4–6):1859–1894, 2012) as the infinitesimal generator of a non-Brownian tug-of-war game. We first construct a class of viscosity solutions of the initial-value problem for bounded and uniformly continuous data.
Félix del Teso +3 more
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