Hardy’s inequality for convex sets: local and nonlocal

Geometric Aspects of Nonlinear Partial Differential Equations

30 August 14:00 - 15:00

Lorenzo Brasco - University of Ferrara

We start by reviewing the classical Hardy inequality for convex sets. In particu-lar, we recall a couple of classical analytic proofs. We then discuss the counterpart of Hardy’s inequality for the case of fractional Sobolev-Slobodecki˘ı spaces, still in the case of open convex subsets of the Euclidean space. In particular, we determine the sharp constant in this inequality, by constructing explicit supersolutions based on the distance function. We also show that this method works only for the mildly nonlocal regime and it gets stuck for the strongly nonlocal one. We conclude by presenting some open problems. Some of the results presented are issued from papers in collaboration with Francesca Bianchi (Ferrara & Parma), Eleonora Cinti (Bologna) and Anna Chiara Zagati (Ferrara & Parma).
Panagiota Daskalopoulos
Columbia University
Alessio Figalli
ETH Zürich
Erik Lindgren
Uppsala University
Henrik Shahgholian
KTH Royal Institute of Technology
Susanna Terracini,
University of Turin


Erik Lindgren

Henrik Shahgholian


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