Results 11 to 20 of about 1,157 (77)
Conformal upper bounds for the eigenvalues of the p‐Laplacian
Journal of the London Mathematical Society, Volume 104, Issue 5, Page 2128-2147, December 2021., 2021 Abstract In this note we present upper bounds for the variational eigenvalues of the p‐Laplacian on smooth domains of complete n‐dimensional Riemannian manifolds and Neumann boundary conditions, and on compact (boundaryless) Riemannian manifolds. In particular, we provide upper bounds in the conformal class of a given metric for 1
Bruno Colbois, Luigi Provenzano
wiley +1 more source
Universal inequalities of the poly-drifting Laplacian on smooth metric measure spaces
Open Mathematics, 2021 In this paper, we study the eigenvalue problem of poly-drifting Laplacian on complete smooth metric measure space (M,⟨,⟩,e−ϕdv)\left(M,\langle ,\rangle ,{e}^{-\phi }{\rm{d}}v), with nonnegative weighted Ricci curvature Ricϕ≥0{{\rm{Ric}}}^{\phi }\ge 0 for
Hou Lanbao +3 more
doaj +1 more source
Eigenfunctions in Finsler Gaussian solitons
Open Mathematics, 2023 Gaussian solitons are important examples in the theory of Riemannian measure space. In the first part, we explicitly characterize the first eigenfunctions of the drift Laplacian in a Gaussian shrinking soliton, which shows that apart from each coordinate
Liu Caiyun, Yin Songting
doaj +1 more source
Dirichlet problems involving the Hardy-Leray operators with multiple polars
Advances in Nonlinear Analysis, 2023 Our aim of this article is to study qualitative properties of Dirichlet problems involving the Hardy-Leray operator ℒV≔−Δ+V{{\mathcal{ {\mathcal L} }}}_{V}:= -\Delta +V, where V(x)=∑i=1mμi∣x−Ai∣2V\left(x)={\sum }_{i=1}^{m}\frac{{\mu }_{i}}{{| x-{A}_{i}| }
Chen Huyuan, Chen Xiaowei
doaj +1 more source
, 2021 In a weighted Killing warped productMn f ×ρR with warping metric 〈 , 〉M+ ρ2 dt, where the warping function ρ is a real positive function defined on Mn and the weighted function f does not depend on the parameter t ∈ R, we use equivariant bifurcation ...
M. Velásquez +2 more
semanticscholar +1 more source
Estimates for eigenvalues of the Neumann and Steklov problems
Advances in Nonlinear Analysis, 2023 We prove Li-Yau-Kröger-type bounds for Neumann-type eigenvalues of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a biharmonic Steklov problem and of the Laplacian, which ...
Du Feng +4 more
doaj +1 more source
On the solutions to p-Poisson equation with Robin boundary conditions when p goes to +∞
Advances in Nonlinear Analysis, 2022 We study the behaviour, when p→+∞p\to +\infty , of the first p-Laplacian eigenvalues with Robin boundary conditions and the limit of the associated eigenfunctions.
Amato Vincenzo +3 more
doaj +1 more source
Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order
Advances in Nonlinear Analysis, 2022 In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully obtain a general inequality for
Du Feng +3 more
doaj +1 more source
Equitable colourings of Borel graphs
Forum of Mathematics, Pi, 2021 Hajnal and Szemerédi proved that if G is a finite graph with maximum degree $\Delta $ , then for every integer $k \geq \Delta +1$ , G has a proper colouring with k colours in which every two colour classes differ in size at most by $1$ ;
Anton Bernshteyn, Clinton T. Conley
doaj +1 more source
Advanced Nonlinear Studies, 2020 We consider elliptic operators with measurable coefficients and Robin boundary conditions on a bounded domain Ω⊂ℝd{\Omega\subset\mathbb{R}^{d}} and show that the first eigenfunction v satisfies v(x)≥δ>0{v(x)\geq\delta>0} for all x∈Ω¯{x\in\overline ...
Arendt Wolfgang +2 more
doaj +1 more source