Hypoellipticity for linear degenerate elliptic systems in Carnot groups and applications

Emily Shores

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Hypoellipticity for linear degenerate elliptic systems in Carnot groups and applications

Emily Shores

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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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Emily Shores. 2005-02-27. Hypoellipticity for linear degenerate elliptic systems in Carnot groups and applications. https://arxiv.org/abs/math/0502569

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