Optimal Hardy inequalities in cones

• Published in: Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 147; no. 1; pp. 89 - 124
• Main Authors: Devyver, Baptiste, Pinchover, Yehuda, Psaradakis, Georgios
• Format: Journal Article
• Language: English
• Published: Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.02.2017; Cambridge University Press
• Subjects: Boundaries; Cones; Inequalities; Mathematical functions; Operators; Optimization; Origins; Smoothness; minimal growth; positive solutions; 35J20; 35P05; Hardy inequality; Secondary 35B09; Primary 35A23

Let Ω be an open connected cone in ℝ n with vertex at the origin. Assume that the Operator is subcritical in Ω, where δΩ is the distance function to the boundary of Ω and μ ⩽ 1/4. We show that under some smoothness assumption on Ω the improved Hardy-type inequality holds true, and the Hardy-weight λ...