English

H\"older estimates for the Neumann problem in a domain with holes and a relation formula between the Dirichlet and Neumann problems

Analysis of PDEs 2019-06-24 v1

Abstract

In this paper we study the dependence of the H\"older estimates on the geometry of a domain with holes for the Neumann problem. For this, we study the H\"older regularity of the solutions to the Dirichlet and Neumann problems in the disk (and in the exterior of the disk), from which we get a relation between harmonic extensions and harmonic functions with prescribed Neumann condition on the boundary of the disk (for both interior and exterior problems).

Keywords

Cite

@article{arxiv.1906.09110,
  title  = {H\"older estimates for the Neumann problem in a domain with holes and a relation formula between the Dirichlet and Neumann problems},
  author = {Victor Cañulef-Aguilar and Duvan Henao},
  journal= {arXiv preprint arXiv:1906.09110},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1901.06174