BMO-regularity for a degenerate transmission problem

Vincenzo Bianca; Edgard A. Pimentel; José Miguel Urbano

doi:10.1007/s13324-023-00867-x

BMO-regularity for a degenerate transmission problem

Vincenzo Bianca, Edgard A. Pimentel, José Miguel Urbano^*

^*Corresponding author for this work

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

1 Scopus citations

Abstract

We examine a transmission problem driven by a degenerate quasilinear operator with a natural interface condition. Two aspects of the problem entail genuine difficulties in the analysis: the absence of representation formulas for the operator and the degenerate nature of the diffusion process. Our arguments circumvent these difficulties and lead to new regularity estimates. For bounded interface data, we prove the local boundedness of weak solutions and establish an estimate for their gradient in BMO -spaces. The latter implies solutions are of class C^{0 , Log - Lip} across the interface. Relaxing the assumptions on the data, we establish local Hölder continuity for the solutions.

Original language	English (US)
Article number	9
Journal	Analysis and Mathematical Physics
Volume	14
Issue number	1
DOIs	https://doi.org/10.1007/s13324-023-00867-x
State	Published - Feb 2024

Bibliographical note

Publisher Copyright:
© 2024, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

BMO gradient estimates
Local boundedness
Log-Lipschitz regularity
p-Laplace operator
Transmission problems

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

Access to Document

10.1007/s13324-023-00867-x

Cite this

@article{ebe62b068c8e47fdb51b52bfff704573,

title = "BMO-regularity for a degenerate transmission problem",

abstract = "We examine a transmission problem driven by a degenerate quasilinear operator with a natural interface condition. Two aspects of the problem entail genuine difficulties in the analysis: the absence of representation formulas for the operator and the degenerate nature of the diffusion process. Our arguments circumvent these difficulties and lead to new regularity estimates. For bounded interface data, we prove the local boundedness of weak solutions and establish an estimate for their gradient in BMO -spaces. The latter implies solutions are of class C0 , Log - Lip across the interface. Relaxing the assumptions on the data, we establish local H{\"o}lder continuity for the solutions.",

keywords = "BMO gradient estimates, Local boundedness, Log-Lipschitz regularity, p-Laplace operator, Transmission problems",

author = "Vincenzo Bianca and Pimentel, {Edgard A.} and Urbano, {Jos{\'e} Miguel}",

note = "Publisher Copyright: {\textcopyright} 2024, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2024",

month = feb,

doi = "10.1007/s13324-023-00867-x",

language = "English (US)",

volume = "14",

journal = "Analysis and Mathematical Physics",

issn = "1664-2368",

publisher = "Springer Science + Business Media",

number = "1",

}

TY - JOUR

T1 - BMO-regularity for a degenerate transmission problem

AU - Bianca, Vincenzo

AU - Pimentel, Edgard A.

AU - Urbano, José Miguel

PY - 2024/2

Y1 - 2024/2

N2 - We examine a transmission problem driven by a degenerate quasilinear operator with a natural interface condition. Two aspects of the problem entail genuine difficulties in the analysis: the absence of representation formulas for the operator and the degenerate nature of the diffusion process. Our arguments circumvent these difficulties and lead to new regularity estimates. For bounded interface data, we prove the local boundedness of weak solutions and establish an estimate for their gradient in BMO -spaces. The latter implies solutions are of class C0 , Log - Lip across the interface. Relaxing the assumptions on the data, we establish local Hölder continuity for the solutions.

AB - We examine a transmission problem driven by a degenerate quasilinear operator with a natural interface condition. Two aspects of the problem entail genuine difficulties in the analysis: the absence of representation formulas for the operator and the degenerate nature of the diffusion process. Our arguments circumvent these difficulties and lead to new regularity estimates. For bounded interface data, we prove the local boundedness of weak solutions and establish an estimate for their gradient in BMO -spaces. The latter implies solutions are of class C0 , Log - Lip across the interface. Relaxing the assumptions on the data, we establish local Hölder continuity for the solutions.

KW - BMO gradient estimates

KW - Local boundedness

KW - Log-Lipschitz regularity

KW - p-Laplace operator

KW - Transmission problems

UR - http://www.scopus.com/inward/record.url?scp=85183053787&partnerID=8YFLogxK

U2 - 10.1007/s13324-023-00867-x

DO - 10.1007/s13324-023-00867-x

M3 - Article

AN - SCOPUS:85183053787

SN - 1664-2368

VL - 14

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

IS - 1

M1 - 9

ER -

BMO-regularity for a degenerate transmission problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this