English

Note about the existence and essential uniqueness of quadrature domains

Analysis of PDEs 2024-05-03 v1

Abstract

This note is intended to explain the proof of two facts about quadrature domains: first, they are essentially unique if they exist; and second, they do exist for a large class of weight functions. The proofs roughly follow Sakai's "Solutions to the obstacle problem as Green potentials," but are presented at an easier level.

Keywords

Cite

@article{arxiv.2405.00737,
  title  = {Note about the existence and essential uniqueness of quadrature domains},
  author = {Hannah Cairns},
  journal= {arXiv preprint arXiv:2405.00737},
  year   = {2024}
}