All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 122

Showing per page

Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle

Milan Práger (1998)

Applications of Mathematics

A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.

Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics

Michael Hitrik, Karel Pravda-Starov (2013)

Annales de l’institut Fourier

For a class of non-selfadjoint h –pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of...

Eigenvalues of polyharmonic operators on variable domains

Davide Buoso, Pier Domenico Lamberti (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a class of eigenvalue problems for polyharmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain perturbations and compute Hadamard-type formulas for the Frechét differentials. We also consider isovolumetric domain perturbations and characterize the corresponding critical domains for the symmetric functions of the eigenvalues. Finally, we prove that balls are...

Eigenvalues of the p -Laplacian in 𝐑 N with indefinite weight

Yin Xi Huang (1995)

Commentationes Mathematicae Universitatis Carolinae

We consider the nonlinear eigenvalue problem - div ( | ∇ u | p - 2 ∇ u ) = λ g ( x ) | u | p - 2 u in 𝐑 N with p > 1 . A condition on indefinite weight function g is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in W 1 , p ( 𝐑 N ) . A nonexistence result is also given for the case p ≥ N .

Elementary linear algebra for advanced spectral problems

Johannes Sjöstrand, Maciej Zworski (2007)

Annales de l’institut Fourier

We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical...

Eliciting harmonics on strings

Steven J. Cox, Antoine Henrot (2008)

ESAIM: Control, Optimisation and Calculus of Variations

One may produce the qth harmonic of a string of length π by applying the 'correct touch' at the node π / q during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is a damper of magnitude b concentrated at π / q . The 'correct touch' is that b for which the modes, that do not vanish at π / q , are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree q - 1 ....

Equations de Fokker-Planck géométriques II : estimations hypoelliptiques maximales

Gilles Lebeau (2007)

Annales de l’institut Fourier

Nous donnons des résultats analytiques sur les propriétés de régularité du laplacien hypoelliptique de Jean-Michel Bismut et plus généralement sur les opérateurs P de type Fokker-Planck géométrique agissant sur le fibré cotangent Σ = T * X d’une variété riemannienne compacte X . En particulier, nous prouvons un résultat d’hypoellipticité maximale pour P , et nous en déduisons des bornes sur la localisation de ses valeurs spectrales.

Currently displaying 41 – 60 of 122