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The resolvent for Laplace-type operators on asymptotically conic spaces

Andrew Hassell, András Vasy (2001)

Annales de l’institut Fourier

Let X be a compact manifold with boundary, and g a scattering metric on X , which may be either of short range or “gravitational” long range type. Thus, g gives X the geometric structure of a complete manifold with an asymptotically conic end. Let H be an operator of the form H = Δ + P , where Δ is the Laplacian with respect to g and P is a self-adjoint first order scattering differential operator with coefficients vanishing at ∂ X and satisfying a “gravitational” condition. We define a symbol calculus for...

The speed of propagation for KPP type problems. I: Periodic framework

Henry Berestycki, François Hamel, Nikolai Nadirashvili (2005)

Journal of the European Mathematical Society

This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain,...

The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent

Yannick Privat, Mario Sigalotti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...

The third order spectrum of the p-biharmonic operator with weight

Khalil Ben Haddouch, Najib Tsouli, Zakaria El Allali (2014)

Applicationes Mathematicae

We show that the spectrum of Δ ² p u + 2 β · ∇ ( | Δ u | p - 2 Δ u ) + | β | ² | Δ u | p - 2 Δ u = α m | u | p - 2 u , where β ∈ ℝ N , under Navier boundary conditions, contains at least one sequence of eigensurfaces.

Currently displaying 61 – 80 of 110