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arXiv · 2207.08509

Why bootstrapping for $J$-holomorphic curves fails in $C^k$

Hansjörg Geiges·Murat Sağlam·Kai Zehmisch
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Abstract

We present a simple example for the failure of the Calder\'on-Zygmund estimate for the $\bar{\partial}$-operator when the Sobolev $(k,p)$-norms are replaced by the $C^k$-norms. This example is discussed in the context of elliptic bootstrapping, Fredholm theory, and the regularity of $J$-holomorphic curves.

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Hansjörg Geiges, Murat Sağlam, Kai Zehmisch. 2022-07-18. Why bootstrapping for $J$-holomorphic curves fails in $C^k$. https://doi.org/10.1007/s13324-022-00775-6

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