Regularity results for nonlocal evolution Venttsel' problems

Standard

Regularity results for nonlocal evolution Venttsel' problems. / Creo, Simone; Lancia, Maria Rosaria; Nazarov, Alexander I. .

In: Fractional Calculus and Applied Analysis, Vol. 23, No. 5, 2020, p. 1416-1430.

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

Author

Creo, Simone ; Lancia, Maria Rosaria ; Nazarov, Alexander I. . / Regularity results for nonlocal evolution Venttsel' problems. In: Fractional Calculus and Applied Analysis. 2020 ; Vol. 23, No. 5. pp. 1416-1430.

BibTeX

@article{f5fc0bf82add400ebee0517b4ec49fb5,

title = "Regularity results for nonlocal evolution Venttsel' problems",

abstract = "We consider parabolic nonlocal Venttsel{\textquoteright} problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution. The nonlocal term can be regarded as a regional fractional Laplacian on the boundary. The regularity results deeply rely on a priori estimates, obtained via the so-called Munchhausen trick, and sophisticated extension theorem for anisotropic weighted Sobolev spaces.",

keywords = "Primary 35K20, 35B65, Secondary 335R02, 35B45, Venttsel{\textquoteright} problems, nonlocal operators, anisotropic weighted Sobolev spaces, piecewise smooth domains, Venttsel' problems",

author = "Simone Creo and Lancia, {Maria Rosaria} and Nazarov, {Alexander I.}",

note = "Publisher Copyright: {\textcopyright} 2020 Diogenes Co., Sofia 2020.",

year = "2020",

doi = "10.1515/fca-2020-0070",

language = "English",

volume = "23",

pages = "1416--1430",

journal = "Fractional Calculus and Applied Analysis",

issn = "1311-0454",

publisher = "De Gruyter",

number = "5",

}

RIS

TY - JOUR

T1 - Regularity results for nonlocal evolution Venttsel' problems

AU - Creo, Simone

AU - Lancia, Maria Rosaria

AU - Nazarov, Alexander I.

PY - 2020

Y1 - 2020

N2 - We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution. The nonlocal term can be regarded as a regional fractional Laplacian on the boundary. The regularity results deeply rely on a priori estimates, obtained via the so-called Munchhausen trick, and sophisticated extension theorem for anisotropic weighted Sobolev spaces.

AB - We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution. The nonlocal term can be regarded as a regional fractional Laplacian on the boundary. The regularity results deeply rely on a priori estimates, obtained via the so-called Munchhausen trick, and sophisticated extension theorem for anisotropic weighted Sobolev spaces.

KW - Primary 35K20

KW - 35B65

KW - Secondary 335R02

KW - 35B45

KW - Venttsel’ problems

KW - nonlocal operators

KW - anisotropic weighted Sobolev spaces

KW - piecewise smooth domains

KW - Venttsel' problems

UR - https://www.degruyter.com/view/journals/fca/23/5/article-p1416.xml?language=en

UR - http://www.scopus.com/inward/record.url?scp=85096301377&partnerID=8YFLogxK

U2 - 10.1515/fca-2020-0070

DO - 10.1515/fca-2020-0070

M3 - Article

VL - 23

SP - 1416

EP - 1430

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

SN - 1311-0454

IS - 5

ER -

ID: 71520778