Estimates for Dirichlet Eigenfunctions

1999/04/01 by M. van den Berg, M. Van Den Berg, E. Bolthausen +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Nonlinear Partial Differential Equations

paper · doi:10.1112/s0024610799007267

Abstract

Estimates for the Dirichlet eigenfunctions near the boundary of an open, bounded set in euclidean space are obtained. It is assumed that the boundary satisfies a uniform capacitary density condition.

Cited by

• On the gradient of the torsion function for elongated cylinders
• Quantitative stability control of the full spectrum of the Dirichlet Laplacian by the second eigenvalue

Related

• On the regularity of Dirac eigenfunctions
• Perturbing the principal Dirichlet eigenfunction
• Interior estimates for the eigenfunctions of the fractional Laplacian on a bounded Euclidean domain
• The sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions
• Efficiency and localisation for the first Dirichlet eigenfunction