Hypoellipticity for linear degenerate elliptic systems in Carnot groups and applications

Details Hypoellipticity for linear degenerate elliptic systems in Carnot groups and applications Hypoellipticity for linear degenerate elliptic systems in Carnot groups and applications

2005-02-27

arxiv.org/abs/math/0502569v1

Mathematics

Analysis of PDEs

27 pages

Scientific paper

We prove that if u is a weak solution to a constant coefficient system (with
strong ellipticity assumed along the horizontal direction) in a Carnot group
(no restriction on the step), then u is actually smooth. We then use this
result to develop blow-up analysis to prove a partial regularity result for
weak solutions of certain non-linear systems.

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