Results 41 to 50 of about 43,034 (224)

An Adaptive Finite Element Method for the Infinity Laplacian [PDF]

, 2014
We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem may be singular, which has prompted us to conduct an a posteriori analysis of the method deriving residual based estimators to drive an adaptive algorithm.
Lakkis, Omar, Pryer, Tristan
openaire   +2 more sources

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

The Dirichlet problem in an unbounded cone-like domain for second order elliptic quasilinear equations with variable nonlinearity exponent

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper we consider the Dirichlet problem for quasi-linear second-order elliptic equation with the $m(x)$-Laplacian and the strong nonlinearity on the right side in an unbounded cone-like domain.
Mikhail Borsuk, Damian Wiśniewski
doaj   +1 more source

Quantum Leaks

, 2005
We show that eigenfunctions of the Laplacian on certain non-compact domains with finite area may localize at infinity--provided there is no extreme level clustering--and thus rule out quantum unique ergodicity for such systems.
Marklof, Jens
core   +2 more sources

The infinity Laplacian, Aronsson's equation and their generalizations [PDF]

Transactions of the American Mathematical Society, 2008
The very interesting paper under review deals with the infinity Laplace equation, the related Aronsson equation and their various generalizations in nonlinear PDE theory. The infinity Laplacian equation \[ \Delta_\infty u:= u_{x_i}u_{x_j}u_{x_ix_j}=0, \] defined for smooth functions \(u\) on some open set \(U\subseteq \mathbb R^n,\) arises originally ...
Barron, E. N., Evans, L. C., Jensen, R.
openaire   +2 more sources

Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver

International Journal for Numerical Methods in Fluids, EarlyView.
A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
wiley   +1 more source

Exponential Decay of Eigenfunctions and Accumulation of Eigenvalues on Manifolds with Axial Analytic Asymptotically Cylindrical Ends [PDF]

, 2010
In this paper we continue our study of the Laplacian on manifolds with axial analytic asymptotically cylindrical ends initiated in~arXiv:1003.2538. By using the complex scaling method and the Phragm\'{e}n-Lindel\"{o}f principle we prove exponential decay
Kalvin, Victor
core  

Asymptotics for logistic-type equations with Dirichlet fractional Laplace operator

, 2021
We study the asymptotics of solutions of logistic type equations with fractional Laplacian as time goes to infinity and as the exponent in nonlinear part goes to infinity.
Klimsiak, Tomasz
core  

Observation of Linear and Nonlinear Light Trapping on Topological Dislocations

Laser &Photonics Reviews, EarlyView.
Topological dislocations are global lattice defects found in various systems ranging from crystals to photonic lattices. This work reports the first observation at optical frequencies of linear modes with tunable localization bound to edge dislocations and their nonlinear counterparts ‐ dislocation solitons. These results reveal an intriguing interplay
S. K. Ivanov, A. V. Kireev, K. Sabour, N. S. Kostyuchenko, S. A. Zhuravitskii, N. N. Skryabin, I. V. Dyakonov, A. A. Kalinkin, V. O. Kompanets, S. P. Kulik, S. V. Chekalin, A. Ferrando, V. N. Zadkov, Y. V. Kartashov   +13 more
wiley   +1 more source

Large solutions of a class of degenerate equations associated with infinity Laplacian

Advanced Nonlinear Studies, 2022
In this article, we investigate the boundary blow-up problem Δ∞hu=f(x,u),inΩ,u=∞,on∂Ω,\left\{\begin{array}{ll}{\Delta }_{\infty }^{h}u=f\left(x,u),& {\rm{in}}\hspace{0.33em}\Omega ,\\ u=\infty ,& {\rm{on}}\hspace{0.33em}\partial \Omega ,\end{array}\right.
Li Cuicui, Liu Fang
doaj   +1 more source