On a class of Rellich inequalities

2004/12/07 by Gerassimos Barbatis, G. Barbatis, Barbatis, G. +3 · 1 citation
Computer Science · Mathematics · #35J20 #35P20 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #math.AP #math.SP #msc:35J20 #msc:35P20

paper · pdf · doi:10.48550/arxiv.math/0412146

15 pages. To appear in J. Comput. Appl. Math

arxiv created 2004/12/07 · openalex publication_date 2004/12/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Rellich and improved Rellich inequalities that involve the distance function from a hypersurface of codimension k, under a certain geometric assumption. In case the distance is taken from the boundary, that assumption is the convexity of the domain. We also discuss the best constant of these inequalities.

Cited by

• Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem

Related

• Finsler-Rellich inequalities involving the distance to the boundary
• Improved Rellich inequalities for the polyharmonic operator
• Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem
• Optimal inequalities between distances in convex projective domains
• Best constants for higher-order Rellich inequalities in L^p(Ω)