Results 11 to 20 of about 43,034 (224)

Monotonicity results for the fractional p-Laplacian in unbounded domains

Bulletin of Mathematical Sciences, 2021
In this paper, we develop a direct method of moving planes in unbounded domains for the fractional p-Laplacians, and illustrate how this new method to work for the fractional p-Laplacians.
Leyun Wu, Mei Yu, Binlin Zhang
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Bernoulli Free Boundary Problem for the Infinity Laplacian [PDF]

SIAM Journal on Mathematical Analysis, 2020
We study the interior Bernoulli free boundary problem for the infinity Laplacian. Our results cover existence, uniqueness, and characterization of solutions (above a threshold representing the "infinity Bernoulli constant"), their regularity, and their relationship with the solutions to the interior Bernoulli problem for the $p$-laplacian.
Crasta G, Fragalà I.
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Infinity Laplacian equations with singular absorptions

Calculus of Variations and Partial Differential Equations, 2022
In this work, we study regularity properties for nonvariational singular elliptic equations ruled by the infinity Laplacian. We obtain optimal $C^{1,α}$ regularity along the free boundary. We also show existence of solutions, nondegeneracy properties and fine geometric estimates for the free boundary.
Damião J. Araújo, Ginaldo S. Sá
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Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in $\protect \mathbb{R}^N$

Comptes Rendus. Mathématique, 2022
In this paper, we consider the following 1-Laplacian problem \[ -\Delta _1 u+V(x)\frac{u}{|u|}= f(x,u),\, x\in \mathbb{R}^N,\, u>0,\ u\in BV\left(\mathbb{R}^N\right), \] where $\Delta _1 u=\mathrm{div}(\tfrac{Du}{|Du|})$, $V$ is a periodic potential and $
Wang, Shi-Ying, Chen, Peng, Li, Lin
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Optimal Lipschitz extensions and the infinity laplacian [PDF]

Calculus of Variations and Partial Differential Equations, 2001
The paper presents results on viscosity solutions of boundary value problems for the so-called infinity Laplacian PDE. Among the results are the characterization of the almost minimizing Lipschitz extension property by means of solutions of such equations as well as several regularity properties for the solutions.
Crandall, M. G., Evans, L. C., Gariepy, R. F.   +2 more
openaire   +1 more source

Inhomogeneous Dirichlet problems involving the infinity-Laplacian

Advances in Differential Equations, 2012
Our purpose in this paper is to provide a self-contained account of the inhomogeneous Dirichlet problem ${\Delta_\infty} u=f(x,u)$ where $u$ represents prescribed continuous data on the boundary of bounded domains. We employ a combination of Perron's method and a priori estimates to give general sufficient conditions on the right-hand side $f$ that ...
Bhattacharya, Bhattacharya, Mohammed, Ahmed   +1 more
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Principal eigenvalue problem for infinity Laplacian in metric spaces

Advanced Nonlinear Studies, 2022
This article is concerned with the Dirichlet eigenvalue problem associated with the ∞\infty -Laplacian in metric spaces. We establish a direct partial differential equation approach to find the principal eigenvalue and eigenfunctions in a proper geodesic
Liu Qing, Mitsuishi Ayato
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Magnetic bottles on the Poincar\'e half-plane: spectral asymptotics [PDF]

, 2007
We consider a magnetic laplacian P(A) on the Poincar\'e half-plane, when the magnetic field dA is infinite at infinity such that P(A) has pure discret spectrum.
Morame, Abderemane, Truc, Francoise
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On asymptotic expansions for the fractional infinity Laplacian [PDF]

Asymptotic Analysis, 2021
We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional ∞-Laplacian [Formula: see text] for [Formula: see text]. This operator has been introduced and first studied in ( Comm. Pure Appl. Math. 65 (2012) 337–380).
del Teso, Félix, Endal, Jørgen, Lewicka, Marta   +2 more
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Parabolic Biased Infinity Laplacian Equation Related to the Biased Tug-of-War

Advanced Nonlinear Studies, 2019
In this paper, we study the parabolic inhomogeneous β-biased infinity Laplacian equation arising from the β-biased tug-of ...
Liu Fang, Jiang Feida
doaj   +1 more source