Cristian Cazacu
University of Bucharest & Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania

In this talk we present some recent results on improved Hardy inequalities for the magnetic $p$-Laplacian due to adding nontrivial magnetic fields. We also show that for Aharonov Bohm magnetic fields the sharp constant in the Hardy inequality becomes strictly larger than in the case of a magnetic-free $p$-Laplacian. In the end we post some remarks with open problems. This exposure is based on a joint work with David Krejčřík (Czech Technical University, Prague, Czech Republic), Nguyen Lam (Memorial University of Newfoundland, Canada) and Ari Laptev (Imperial College London, United Kingdom). Partially supported by CNCS-UEFISCDI Romania, Grant No. PN-III-P1-1.1-TE-2021-1539.