Estimates for the Lq-mixed problem in C1,1-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

R. M. Brown
, L. D. Croyle

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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
Pages (from-to)	181-193
Number of pages	13
Journal	Complex Variables and Elliptic Equations
Volume	66
Issue number	2
DOIs	https://doi.org/10.1080/17476933.2019.1709971
State	Published - 2021

Bibliographical note

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

Funding

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

Funders	Funder number
Simons Foundation	422756

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

Access to Document

10.1080/17476933.2019.1709971

Cite this

@article{0acec3f0d72743799010fa98c854dd7d,

title = "Estimates for the Lq-mixed problem in C1,1-domains",

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.).",

keywords = "35J25, Besov spaces, Laplace's equation, Mixed boundary value problem, Zaremba's problem, harmonic analysis",

author = "Brown, \{R. M.\} and Croyle, \{L. D.\}",

note = "Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2021",

doi = "10.1080/17476933.2019.1709971",

language = "English",

volume = "66",

pages = "181--193",

number = "2",

}

TY - JOUR

T1 - Estimates for the Lq-mixed problem in C1,1-domains

AU - Brown, R. M.

AU - Croyle, L. D.

PY - 2021

Y1 - 2021

N2 - 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.).

AB - 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.).

KW - 35J25

KW - Besov spaces

KW - Laplace's equation

KW - Mixed boundary value problem

KW - Zaremba's problem

KW - harmonic analysis

UR - https://www.scopus.com/pages/publications/85078604003

UR - https://www.scopus.com/pages/publications/85078604003#tab=citedBy

U2 - 10.1080/17476933.2019.1709971

DO - 10.1080/17476933.2019.1709971

M3 - Article

AN - SCOPUS:85078604003

SN - 1747-6933

VL - 66

SP - 181

EP - 193

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 2

ER -