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International Workshop on Critical Phenomena (7/2 - 7/4) ( 2018-06-30 )
News Content:
Venue: SA223, Science Building I, NCTU
Limiting Sobolev Estimates for Vector Fields and Canceling Differ-
ential Operators
Jean Van Schaftingen (Universit ́e catholique de Louvain)
Abstract:
In the limiting case p = 1 of the Calder ́on-Zygmund estimates, the L1
norm of an homoge-neous vector differential operator cannot be used to estimate other derivatives of the same
order. If one is interested in Sobolev-type estimates on lower-order derivatives, these hold (Bourgain-Brezis estimates) or fail depending on the operator. The question whether the
latter estimate holds can be determined on any homogeneous vector differential operator by determining whether it satisfies a new canceling condition in addition to the classical ellipticity
condition. This result unifies classes of known inequalities and extends to the case of Hardy inequalitie
File:0702agenda.pdf
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