Estimates for the $L^q$-mixed problem in $C^{1,1}$-domains

R. M. Brown; L. D. Croyle

doi:10.1080/17476933.2019.1709971

Estimates for the $L^q$-mixed problem in $C^{1,1}$-domains

Analysis of PDEs 2023-03-27 v1

Authors: R. M. Brown , L. D. Croyle

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Abstract

We consider the $L^q$ -mixed problem in domains in ${\bf R}^n$ with $C^ {1,1}$ -boundary. We assume that the boundary between the sets where we specify Neumann and Dirichlet data is Lipschitz. With these assumptions, we show that we may solve the $L^q$ -mixed problem for $q$ in the range $1<q < n/(n-1)$ .

Keywords

lq-mixed problem c1,1-domains neumann data dirichlet data lipschitz boundary partial differential equations

Cite

@article{arxiv.1902.08843,
  title  = {Estimates for the $L^q$-mixed problem in $C^{1,1}$-domains},
  author = {R. M. Brown and L. D. Croyle},
  journal= {arXiv preprint arXiv:1902.08843},
  year   = {2023}
}

Comments

15 pages

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