On $C^1$-approximability of functions by solutions of second order elliptic equations on plane compact sets and $C$-analytic capacity

Petr V. Paramonov; Xavier Tolsa

On $C^1$-approximability of functions by solutions of second order elliptic equations on plane compact sets and $C$-analytic capacity

Classical Analysis and ODEs 2018-11-16 v1 Analysis of PDEs

Authors: Petr V. Paramonov , Xavier Tolsa

Abstract

Criteria for approximability of functions by solutions of homogeneous second order elliptic equations (with constant complex coefficients) in the norms of the Whitney $C^1$ -spaces on compact sets in $\mathbb R^2$ are obtained in terms of the respective $C^1$ -capacities. It is proved that the mentioned $C^1$ -capacities are comparable to the classic $C$ -analytic capacity, and so have a proper geometric measure characterization.

Keywords

c1-approximation second order elliptic equations whitney c1-spaces plane compact sets c-analytic capacity geometric measure characterization

Cite

@article{arxiv.1811.06288,
  title  = {On $C^1$-approximability of functions by solutions of second order elliptic equations on plane compact sets and $C$-analytic capacity},
  author = {Petr V. Paramonov and Xavier Tolsa},
  journal= {arXiv preprint arXiv:1811.06288},
  year   = {2018}
}

On $C^1$-approximability of functions by solutions of second order elliptic equations on plane compact sets and $C$-analytic capacity

Abstract

Keywords

Cite

Related papers