Regularity of Weak Solutions to Nondiagonal Elliptic Systems with Composite Boundary Conditions

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Regularity of Weak Solutions to Nondiagonal Elliptic Systems with Composite Boundary Conditions. / Arkhipova, A. A.; Grishina, G. V.

In: Journal of Mathematical Sciences (United States), Vol. 247, No. 6, 01.06.2020, p. 791-819.

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

Author

Arkhipova, A. A. ; Grishina, G. V. / Regularity of Weak Solutions to Nondiagonal Elliptic Systems with Composite Boundary Conditions. In: Journal of Mathematical Sciences (United States). 2020 ; Vol. 247, No. 6. pp. 791-819.

BibTeX

@article{951ad9d4040749738ed1a348bc8df570,

title = "Regularity of Weak Solutions to Nondiagonal Elliptic Systems with Composite Boundary Conditions",

abstract = "We consider a model problem in a half-ball for linear and quasilinear elliptic systems of equations with nondiagonal principal matrix. It is assumed that the components of the solution are interconnected by Dirichlet and Neumann type boundary conditions through some matrix on the planar boundary of the half-ball. We establish the H{\"o}lder continuity of weak solutions to linear systems and the partial regularity of weak solutions to quasilinear systems. To treat such composite boundary conditions, we apply a modification of the method of A-harmonic approximations adapted to problems under consideration.",

author = "Arkhipova, {A. A.} and Grishina, {G. V.}",

year = "2020",

month = jun,

day = "1",

doi = "10.1007/s10958-020-04839-5",

language = "English",

volume = "247",

pages = "791--819",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "6",

}

RIS

TY - JOUR

T1 - Regularity of Weak Solutions to Nondiagonal Elliptic Systems with Composite Boundary Conditions

AU - Arkhipova, A. A.

AU - Grishina, G. V.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - We consider a model problem in a half-ball for linear and quasilinear elliptic systems of equations with nondiagonal principal matrix. It is assumed that the components of the solution are interconnected by Dirichlet and Neumann type boundary conditions through some matrix on the planar boundary of the half-ball. We establish the Hölder continuity of weak solutions to linear systems and the partial regularity of weak solutions to quasilinear systems. To treat such composite boundary conditions, we apply a modification of the method of A-harmonic approximations adapted to problems under consideration.

AB - We consider a model problem in a half-ball for linear and quasilinear elliptic systems of equations with nondiagonal principal matrix. It is assumed that the components of the solution are interconnected by Dirichlet and Neumann type boundary conditions through some matrix on the planar boundary of the half-ball. We establish the Hölder continuity of weak solutions to linear systems and the partial regularity of weak solutions to quasilinear systems. To treat such composite boundary conditions, we apply a modification of the method of A-harmonic approximations adapted to problems under consideration.

UR - http://www.scopus.com/inward/record.url?scp=85084975170&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-04839-5

DO - 10.1007/s10958-020-04839-5

M3 - Article

AN - SCOPUS:85084975170

VL - 247

SP - 791

EP - 819

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 62144204