## Abstract

We consider the (Formula presented.) -mixed problem in domains in (Formula presented.) with (Formula presented.) -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 (Formula presented.) -mixed problem for q in the range (Formula presented.).

Original language | English |
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Pages (from-to) | 181-193 |

Number of pages | 13 |

Journal | Complex Variables and Elliptic Equations |

Volume | 66 |

Issue number | 2 |

DOIs | |

State | Published - 2021 |

### Bibliographical note

Funding Information:R. M. Brown is partially supported by the Simons Foundation, Collaboration Grants for Mathematicians, grant number #422756.

Publisher Copyright:

© 2020 Informa UK Limited, trading as Taylor & Francis Group.

## Keywords

- 35J25
- Besov spaces
- Laplace's equation
- Mixed boundary value problem
- Zaremba's problem
- harmonic analysis

## ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics

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