An optimal lower bound in fractional spectral geometry for planar sets with topological constraints

DOI10.1112/jlms.12814arXiv2301.08017OpenAlexW4386485623MaRDI QIDQ6199291

Francesca Bianchi, Lorenzo Brasco

Publication date: 23 February 2024

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.08017

Mathematics Subject Classification ID

Eigenvalue problems for linear operators (47A75) Systems of functional equations and inequalities (39B72) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On fractional capacities relative to bounded open Lipschitz sets
• Hitchhiker's guide to the fractional Sobolev spaces
• Scattering length for stable processes
• Estimate on the fundamental frequency of a drum
• Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval
• Stability of variational eigenvalues for the fractional \(p\)-Laplacian
• Brownian motion and eigenvalues for the Dirichlet Laplacian
• Scattering length and perturbations of \(-\Delta\) by positive potentials
• A note on Hayman's theorem on the bass note of a drum
• Brownian motion and the fundamental frequency of a drum
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• An estimate in the spirit of Poincaré's inequality
• Extensions for Sobolev mappings between manifolds
• The fractional Makai-Hayman inequality
• A quantitative stability estimate for the fractional Faber-Krahn inequality
• The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets
• A note on homogeneous Sobolev spaces of fractional order
• The abstract Lewy-Stampacchia inequality and applications
• Optimal partition problems for the fractional Laplacian
• On Strong Barriers and an Inequality of Hardy for Domains in R ⁿ
• The First Eigenvalue of the Laplacian for Plane Domains
• Some bounds for principal frequency
• Fractional Sobolev Spaces and Inequalities
• On simple eigenvalues of the fractional Laplacian under removal of small fractional capacity sets
• Sharp Fractional Hardy Inequalities in Half-Spaces
• A lower estimation of the principal frequencies of simply connected membranes
• Sobolev Spaces
• A First Course in Fractional Sobolev Spaces

This page was built for publication: An optimal lower bound in fractional spectral geometry for planar sets with topological constraints