Series expansion for L^p Hardy inequalities

By G. Barbatis, Stathis Filippas, A. Tertikas. 2003

110 citations recorded by the source corpus.

We consider a general class of sharp $L^p$ Hardy inequalities in $\R^N$ involving distance from a surface of general codimension $1\leq k\leq N$. We show that we can succesively improve them by adding to the right hand side a lower order term with optimal weight and best constant. This leads to an infinite series improvement of $L^p$ Hardy inequalities.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/58e276c5ce72359a04138f42c4ff492176835401

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Hardy inequalities for general elliptic operators with improvements (2008, background): “In the last few years improved versions of the above inequalities have been obtained, in the sense that non-negative terms are added to the right hand sides of the inequalities; see [BV], [BM], [ BFT ], [BMS],[FT],[FHT],[VS].”
Hardy-type inequalities related to degenerate elliptic differential operators (2006, background): “Furthermore, our main results represent a generalization of some results contained in [4, 5].”
Estimates for the optimal constants in multipolar Hardy inequalities for Schrödinger and Dirac operators (2008, background): “Huge efforts have been done over the past years to improve on Hardy’s inequality, but mostly in the case of a single singularity: see [22, 3, 4, 15, 23].”
Scale invariance structures of the critical and the subcritical Hardy inequalities and their improvements (2017, background): “holds for all u ∈ D 0 (BN R (0)), where D 0 (BN R (0)) is the completion of C∞ 0 (BN R (0)) with respect to the norm ‖∇(·)‖LN (BN R (0)), see [2,3,15,18,19,23].”