$${\text {VMO}}$$ Spaces Associated with Neumann Laplacian

Parabolic Equations with Vmo Coefficients in Spaces with Mixed Norms

An Lq(Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class V MOx, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p = q.

Spectral Stability of the Neumann Laplacian

We prove the equivalence of Hardyand Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also prove that if one perturbs the boundary of the region within a uniform Hölder category then the eigenvalues of the Neumann Laplacian change by a...

On the semiclassical 3D Neumann Laplacian with variable magnetic field

Magnetic Neumann Laplacian on a sharp cone

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture α and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit α → 0 and establish a full asymptotic...

Spectrum of the ∂-neumann Laplacian on Polydiscs

The spectrum of the ∂-Neumann Laplacian on a polydisc in C is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, some of which, in particular the smallest ones, are of infinite multiplicity.