Balls minimize trace constants in BV

2013/01/24 by Cianchi, Andrea, Ferone, Vincenzo, Nitsch, Carlo +1
#26B30 #46E35 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1301.5770

Abstract

Balls are shown to have the smallest optimal constant, among all admissible Euclidean domains, in Poincaré type boundary trace inequalities for functions of bounded variation with vanishing median or mean value.

Related

• Poincaré trace inequalities in BV(\mathbb Bⁿ) with nonstandard normalization
• Exact constants in Poincare type inequalities for functions with zero mean boundary traces
• Trace theorems for functions of bounded variation in metric spaces
• Characterization of balls as minimizers of an endpoint Gagliardo seminorm on the boundary
• Inequalities for BV^\mathbbA -Functions