Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 2 June 2020Accepted: 16 September 2021Published online: 05 January 2022Keywordseigenvalue problem, domain decomposition, dimension reduction, subspace methodAMS Subject Headings65F15Publication DataISSN (print): 0036-1429ISSN (online): 1095-7170Publisher: Society for Indu...

We review some results about the first eigenvalue of the infinity Laplacian operator and its first eigenfunctions in a general norm context. Those results are obtained in collaboration with several authors: V. Ferone, P. Juutinen and B. Kawohl (see [BFK], [BK1], [BJK] and [BK2]). In section 5 we make some remarks on the simplicity of the first eigenvalue of ∆∞: this will be the object of a join...

Let B be a Borel subset of R with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A1 be the time spent by Brownian motion in a closed cone with vertex 0 until time one. We show that limu→0 logP (A1 < u)/ log u = 1/ξ where ξ is defined in terms of the first eigenvalue of the Laplacian in a compact domain. Eigenvalues of the ...

We study the global structure of the set of radial solutions of a nonlinear Dirichlet eigenvalue problem involving the p-Laplacian with p > 2, in the unit ball of RN , N > 1. We show that all non-trivial radial solutions lie on smooth curves of respectively positive and negative solutions, bifurcating from the first eigenvalue of a weighted p-linear problem. Our approach involves a local bifurc...

Nested split and double nested graphs (commonly named nested graphs) are considered. General statements regarding the signless Laplacian spectra are proven, and the nested graphs whose second largest signless Laplacian eigenvalue is bounded by a fixed integral constant are studied. Some sufficient conditions are provided and a procedure for classifying such graphs in particular cases is provide...

We study the eigenvalue asymptotics of a Neumann Laplacian-A$ in unbounded regions 0 of R2 with cusps at infinity (a typical example is a={(~, y)~R~:x>l, Iyl-ce-" I}) and prove that NE(A:)-NE(HY)+ E/2 Vol(Q), where HV is the canonical one-dimensional Schrodinger operator associated to the problem. We establish a similar formula for manifolds with cusps and derive the eigenvalue asymptotics of a...

We prove a CR version of the Obata’s result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian manifold which satisfies a Lichnerowicz type condition and has a divergence free pseudohermitian torsion. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of the pse...

The Seiberg-Witten equations are studied from the viewpoint of gauge potential decomposition. We find a determinant equation ∆Aμ = −λAμ for the twisting U(1) potential Aμ of the Seiberg-Witten theory, which is in itself an eigenvalue problem of the Laplacian operator, with the eigenvalue being the vacuum expectation value of the field function, λ = ‖Φ‖ /2. This establishes a direct relationship...

This paper presents some bounds on the number of Laplacian eigenvalues contained in various subintervals of [0, n] by using the matching number and edge covering number for G, and asserts that for a connected graph the Laplacian eigenvalue 1 appears with certain multiplicity. Furthermore, as an application of our result (Theorem 13), Grone and Merris’ conjecture [The Laplacian spectrum of graph...