Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries

Murat Akman; John Lewis; Andrew Vogel

doi:10.1080/03605302.2022.2056704

Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries

Murat Akman, John Lewis, Andrew Vogel

Department of Mathematics

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

Abstract

Let (Formula presented.) denote Euclidean n space and given k a positive integer let (Formula presented.) be a k-dimensional plane with (Formula presented.) If (Formula presented.) we first study the Martin boundary problem for solutions to the p-Laplace equation (called p-harmonic functions) in (Formula presented.) relative to (Formula presented.) We then use the results from our study to extend the work of Wolff on the failure of Fatou type theorems for p-harmonic functions in (Formula presented.) to p-harmonic functions in (Formula presented.) when (Formula presented.) Finally, we discuss generalizations of our work to solutions of p-Laplace type PDE (called (Formula presented.) -harmonic functions).

Original language	English (US)
Pages (from-to)	1457-1503
Number of pages	47
Journal	Communications in Partial Differential Equations
Volume	47
Issue number	7
DOIs	https://doi.org/10.1080/03605302.2022.2056704
State	Published - 2022

Keywords

Fatou theorem
Gap series
p-harmonic function
p-harmonic measure
radial limits

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1080/03605302.2022.2056704

Cite this

@article{cc6759171faf453dbdaf25d954d8ced4,

title = "Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries",

abstract = "Let (Formula presented.) denote Euclidean n space and given k a positive integer let (Formula presented.) be a k-dimensional plane with (Formula presented.) If (Formula presented.) we first study the Martin boundary problem for solutions to the p-Laplace equation (called p-harmonic functions) in (Formula presented.) relative to (Formula presented.) We then use the results from our study to extend the work of Wolff on the failure of Fatou type theorems for p-harmonic functions in (Formula presented.) to p-harmonic functions in (Formula presented.) when (Formula presented.) Finally, we discuss generalizations of our work to solutions of p-Laplace type PDE (called (Formula presented.) -harmonic functions).",

keywords = "Fatou theorem, Gap series, p-harmonic function, p-harmonic measure, radial limits",

author = "Murat Akman and John Lewis and Andrew Vogel",

note = "Publisher Copyright: {\textcopyright} 2022 The Author(s). Published with license by Taylor & Francis Group, LLC.",

year = "2022",

doi = "10.1080/03605302.2022.2056704",

language = "English (US)",

volume = "47",

pages = "1457--1503",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "7",

}

TY - JOUR

T1 - Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries

AU - Akman, Murat

AU - Lewis, John

AU - Vogel, Andrew

PY - 2022

Y1 - 2022

N2 - Let (Formula presented.) denote Euclidean n space and given k a positive integer let (Formula presented.) be a k-dimensional plane with (Formula presented.) If (Formula presented.) we first study the Martin boundary problem for solutions to the p-Laplace equation (called p-harmonic functions) in (Formula presented.) relative to (Formula presented.) We then use the results from our study to extend the work of Wolff on the failure of Fatou type theorems for p-harmonic functions in (Formula presented.) to p-harmonic functions in (Formula presented.) when (Formula presented.) Finally, we discuss generalizations of our work to solutions of p-Laplace type PDE (called (Formula presented.) -harmonic functions).

AB - Let (Formula presented.) denote Euclidean n space and given k a positive integer let (Formula presented.) be a k-dimensional plane with (Formula presented.) If (Formula presented.) we first study the Martin boundary problem for solutions to the p-Laplace equation (called p-harmonic functions) in (Formula presented.) relative to (Formula presented.) We then use the results from our study to extend the work of Wolff on the failure of Fatou type theorems for p-harmonic functions in (Formula presented.) to p-harmonic functions in (Formula presented.) when (Formula presented.) Finally, we discuss generalizations of our work to solutions of p-Laplace type PDE (called (Formula presented.) -harmonic functions).

KW - Fatou theorem

KW - Gap series

KW - p-harmonic function

KW - p-harmonic measure

KW - radial limits

UR - http://www.scopus.com/inward/record.url?scp=85131181208&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85131181208&partnerID=8YFLogxK

U2 - 10.1080/03605302.2022.2056704

DO - 10.1080/03605302.2022.2056704

M3 - Article

AN - SCOPUS:85131181208

SN - 0360-5302

VL - 47

SP - 1457

EP - 1503

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 7

ER -

Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this