English

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

Analysis of PDEs 2023-01-12 v1 Symplectic Geometry

Abstract

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

Keywords

Cite

@article{arxiv.2207.08509,
  title  = {Why bootstrapping for $J$-holomorphic curves fails in $C^k$},
  author = {Hansjörg Geiges and Murat Sağlam and Kai Zehmisch},
  journal= {arXiv preprint arXiv:2207.08509},
  year   = {2023}
}

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8 pages