Hardy inequalities for magnetic $p$-Laplacians

Abstract

We establish improved Hardy inequalities for the magnetic $p$-Laplacian due to adding nontrivial magnetic fields. We also prove 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. We also post some remarks with open problems.

Some of the conjectures from the previous version resolved with help of the new author added

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