Results 221 to 230 of about 1,336,458 (254)

A multiplicity results for a singular equation involving the p(x)-Laplace operator

, 2017
The purpose of this paper is to study the singular problem involving the p(x)-Laplace operator:(Section.Display) where be a bounded domain with boundary, is a positive parameter and p(x), and f(x, u) are assumed to satisfy the assumptions (H0)–(H4) in ...
K. Saoudi, A. Ghanmi
semanticscholar   +1 more source

Maximum principle for Hadamard fractional differential equations involving fractional Laplace operator

Mathematical methods in the applied sciences, 2019
The purpose of the current study is to investigate IBVP for spatial‐time fractional differential equation with Hadamard fractional derivative and fractional Laplace operator(−Δ)β. A new Hadamard fractional extremum principle is established.
Guotao Wang, Xueyan Ren, D. Baleanu
semanticscholar   +1 more source

The Laplace Operator

2018
The fundamental properties of harmonic and subharmonic functions are given together with maximum principles, the representation of solutions of the Poisson equation, Weyl’s lemma and Perron’s method for proving existence of solutions of the Dirichlet problem.
David E. Edmunds, W. Desmond Evans
openaire   +2 more sources

Extension technique for complete Bernstein functions of the Laplace operator

, 2017
We discuss the representation of certain functions of the Laplace operator $$\Delta $$Δ as Dirichlet-to-Neumann maps for appropriate elliptic operators in half-space.
M. Kwaśnicki, J. Mucha
semanticscholar   +1 more source

On The Attainable Eigenvalues of the Laplace Operator

SIAM Journal on Mathematical Analysis, 1999
We consider the subset E of $\RR^2$ of all points whose first and second components, respectively, coincide with the first and second eigenvalues of the Laplace operator $-\Delta$ with zero boundary conditions on domains of $\RR^N$ with prescribed measure. We show that the set E is closed in $\RR^2$.
D. Bucur, BUTTAZZO, GIUSEPPE, I. Figueiredo   +2 more
openaire   +2 more sources

Convergence of Inverse Power Method for First Eigenvalue of p-Laplace Operator

, 2016
In this article, convergence of an iterative scheme to approximate the first eigenfunction and related eigenvalue for p-Laplace operator is shown. Moreover, numerical examples are presented that show the efficiency and accuracy of the algorithm.
Farid Bozorgnia
semanticscholar   +1 more source

The Eigenvalue Problem for the Laplace Operator [PDF]

, 1998
We use Rellich’s embedding theorem to show that every L 2 function on an open ,fl Ω ⊂ ℝ d can be expanded in terms of eigenfunctions of the Laplace operator on Ω.
openaire   +1 more source

Viewing the Steklov eigenvalues of the Laplace operator as critical Neumann eigenvalues

, 2014
We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of boundary mass concentration. We discuss the asymptotic behavior of the Neumann eigenvalues in a ball and we deduce that the Steklov eigenvalues ...
P. D. Lamberti, Luigi Provenzano
semanticscholar   +1 more source

Strong Uniqueness for Laplace and Bi-Laplace Operators in the Limit Case

2001
In this article we study some limiting cases of strong unique continuation for inequalities of the type $$ \left| {\Delta u\left( x \right)} \right| \leqslant \frac{A} {{\left| x \right|^2 }}\left| {u\left( x \right)} \right| + \frac{B} {{\left| x \right|}}\left| {\nabla u\left( x \right)} \right| x \in \Omega , $$ (1.1) or $$ \left ...
COLOMBINI, FERRUCCIO, GRAMMATICO C.
openaire   +3 more sources

On Problems Driven by the $$(p(\cdot ),q(\cdot ))$$-Laplace Operator

, 2020
C. Vetro, F. Vetro
semanticscholar   +1 more source