Local Hardy and Rellich inequalities for sums of squares of vector\n fields

2016/01/21 by Michael Ruzhansky, Durvudkhan Suragan, Ruzhansky, Michael +1
Mathematics · Engineering · #Advanced Harmonic Analysis Research #Stability and Controllability of Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1601.06157

Abstract

We prove local refined versions of Hardy's and Rellich's inequalities as well\nas of uncertainty principles for sums of squares of vector fields on bounded\nsets of smooth manifolds under certain assumptions on the vector fields. We\nalso give some explicit examples, in particular, for sums of squares of vector\nfields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.\n

Related

• Global solvability and propagation of regularity of sums of squares on compact manifolds
• Subelliptic geometric Hardy type inequalities on half-spaces and convex\n domains
• Hardy-Poincar 'e, Rellich and Uncertainty principle inequalities on\n Riemannian manifolds
• Hardy's theorem for compact Lie groups
• A note on precised Hardy inequalities on Carnot groups and Riemannian manifolds