Hypoellipticity and loss of derivatives with Appendix Analyticity and loss of derivatives

Details Hypoellipticity and loss of derivatives with Appendix Analyticity and loss of derivatives Hypoellipticity and loss of derivatives with Appendix Analyticity and loss of derivatives

2006-01-26

arxiv.org/abs/math/0601646v1

Annals of Mathematics vol. 162 no. 2, September 2005, pp. 943-986

Mathematics

Analysis of PDEs

44 pages including appendix

Scientific paper

For each value of k, two complex vector fields satisfying the bracket
condition are exhibited the sum of whose squares is hypoelliptic but not
subelliptic - in fact the operator loses k-1 derivatives in Sobolev norms. In
the Appendix it is proven that this operator is analytic hypoelliptic.

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