Results 301 to 310 of about 1,096,670 (333)

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

MULTIPLE EIGENVALUES OF THE LAPLACE OPERATOR [PDF]

Mathematics of the USSR-Sbornik, 1988
The estimates from above for the multiplicity of the eigenvalues of the Schrödinger operators on compact Riemannian two-dimensional manifolds are obtained. The paper contains also several examples illustrating the sharpness of the results.
openaire   +2 more sources

Fractional Laplace Operator and Meijer G-function

, 2015
We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace operator maps Meijer G-functions of $$|x|^2$$|x|2, or generalized ...
Bartłomiej Dyda, A. Kuznetsov, M. Kwaśnicki   +2 more
semanticscholar   +1 more source

The Laplace Operator

2017
We consider what is perhaps the most important of all partial differential operators, theLaplace operator (Laplacian) on \(\mathbb {R}^n\).
openaire   +2 more sources

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

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

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

An equivalence theorem for a K-functional constructed by Beltrami–Laplace operator on symmetric spaces

, 2020
S. El Ouadih
semanticscholar   +1 more source

THE LAPLACE OPERATOR

Introduction to Partial Differential Equations, 2020
S. Meda
semanticscholar   +1 more source