Results 51 to 60 of about 43,034 (224)

Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We study eigenvalue problems for the de Rham complex on varying three‐dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non‐constant coefficients. We provide Hadamard‐type formulas for the shape derivatives under weak regularity assumptions on the domain and its ...
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron   +2 more
wiley   +1 more source

Convexity Property of Finsler Infinity Harmonic Functions

International Journal of Differential Equations
In this paper, we investigate the convexity property of viscosity solutions to a homogeneous normalized Finsler infinity Laplacian equation. Weak and strong forms for convexity property have been addressed.
Benyam Mebrate
doaj   +1 more source

Odometer of long-range sandpiles in the torus: mean behaviour and scaling limits [PDF]

, 2018
In \cite{Cipriani2016}, the authors proved that with the appropriate rescaling, the odometer of the (nearest neighbours) Divisible Sandpile in the unit torus converges to the bi-Laplacian field.
Chiarini, Leandro, Jara, Milton, Ruszel, Wioletta   +2 more
core   +1 more source

Ruled strips with asymptotically diverging twisting

, 2018
We consider the Dirichlet Laplacian in a two-dimensional strip composed of segments translated along a straight line with respect to a rotation angle with velocity diverging at infinity. We show that this model exhibits a "raise of dimension" at infinity
de Aldecoa, Rafael Tiedra, Krejcirik, David   +1 more
core   +1 more source

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
wiley   +1 more source

Large time behavior for $p(x)$-Laplacian equations with irregular data

Electronic Journal of Differential Equations, 2015
We study the large time behavior of solutions to p(x)-Laplacian equations with irregular data. Under proper assumptions, we show that the entropy solution of parabolic p(x)-Laplacian equations converges in $L^q(\Omega)$ to the unique stationary ...
Xiaojuan Chai, Haisheng Li, Weisheng Niu
doaj  

General Existence of Solutions to Dynamic Programming Principle [PDF]

, 2013
We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear partial differential equations including the infinity Laplacian, mean curvature
Liu, Qing, Schikorra, Armin
core  

Fractional Infinity Laplacian with Obstacle

This paper deals with the obstacle problem for the fractional infinity Laplacian with nonhomogeneous term $f(u)$, where $f:\mathbb{R}^+ \mapsto \mathbb{R}^+$: $$\begin{cases} L[u]=f(u) &\qquad in \{u>0\}\\ u \geq 0 &\qquad in\, Ω\\ u=g &\qquad on\, \partial Ω\end{cases},$$ with $$L[u](x)=\sup_{y\in Ω,\,y\neq x}\dfrac{u(y)-u(x)}{|y-x|^α}+\
Dweik, Samer, Sabra, Ahmad
openaire   +2 more sources

On the evolution governed by the infinity Laplacian [PDF]

Mathematische Annalen, 2006
The purpose of this paper is to establish the basic results concerning existence, uniqueness, regularity, and a Harnack inequality of viscosity solutions of the degenerate and singular parabolic equation \[ u_t=\left( D^2 u \frac {Du}{| Du| }\right)\cdot \frac {Du}{| Du| }, \] where \(u = u(x,t)\), \(Du=(\frac{\partial u}{\partial x_1},\dots,\frac ...
Juutinen, Petri, Kawohl, Bernd
openaire   +1 more source

Regularity of Viscosity Solutions of the Biased Infinity Laplacian Equation

Analysis in Theory and Applications, 2023
In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war.
Liu, Fang, Meng, Fei, Chen, Xiaoyan
openaire   +2 more sources