- 06-327 Roberta Bosi, Jean Dolbeault, Maria J. Esteban.
- Estimates for the optimal constants in multipolar Hardy inequalities
for Schrödinger and Dirac operators.
Nov 10, 06
(auto. generated ps),
of related papers
Abstract. By expanding squares, we prove several Hardy inequalities with two
critical singularities and constants which explicitly depend upon the
distance between the two singularities. These inequalities involve
the L2 norm. Such results are generalized to an arbitrary number of
singularities and compared with standard results given by the IMS
method. The generalized version of Hardy inequalities with several
singularities is equivalent to some spectral information on a
Schrödinger operator involving a potential with several inverse
square singularities. We also give a generalized Hardy inequality for
Dirac operators in the case of a potential having several
singularities of Coulomb type, which are critical for Dirac operators.