Hypoellipticity for linear degenerate elliptic systems in Carnot groups and applications

2005/02/27 by Emily Shores, Shores, Emily · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #msc:35

paper · pdf · doi:10.48550/arxiv.math/0502569

27 pages

arxiv created 2005/02/27 · arxiv updated 2009/12/01

Abstract

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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