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A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity. / Arkhipova, A. A.

In: Izvestiya RAN, ser. Matematika, Vol. 68, No. 2, 01.03.2004, p. 243-258.

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

Harvard

Arkhipova, AA 2004, 'A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity', Izvestiya RAN, ser. Matematika, vol. 68, no. 2, pp. 243-258. https://doi.org/10.1070/IM2004v068n02ABEH000473

APA

Arkhipova, A. A. (2004). A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity. Izvestiya RAN, ser. Matematika, 68(2), 243-258. https://doi.org/10.1070/IM2004v068n02ABEH000473

Vancouver

Arkhipova AA. A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity. Izvestiya RAN, ser. Matematika. 2004 Mar 1;68(2):243-258. https://doi.org/10.1070/IM2004v068n02ABEH000473

Author

Arkhipova, A. A. / A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity. In: Izvestiya RAN, ser. Matematika. 2004 ; Vol. 68, No. 2. pp. 243-258.

BibTeX

@article{d23e1c5775f1475eab249939ea0805ab,
title = "A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity",
abstract = "We consider quasilinear elliptic non-diagonal systems of equations with strong non-linearity with respect to the gradient. We have already shown that the generalized solution of this problem is H{\"o}lder continuous in the neighbourhood of points of the domain at which the norm of the gradient of the solution is sufficiently small in the Morrey space L 2,n-2. We estimate the H{\"o}lder norm of the solution in the neighbourhood of such points in terms of its norm in the Sobolev space W 2 1. We obtain a similar result under the Dirichlet boundary condition for points situated in the neighbourhood of the boundary.",
author = "Arkhipova, {A. A.}",
year = "2004",
month = mar,
day = "1",
doi = "10.1070/IM2004v068n02ABEH000473",
language = "English",
volume = "68",
pages = "243--258",
journal = "Izvestiya Mathematics",
issn = "1064-5632",
publisher = "IOP Publishing Ltd.",
number = "2",

}

RIS

TY - JOUR

T1 - A priori estimates near the boundary for the solutions of non-diagonal elliptic systems with strong non-linearity

AU - Arkhipova, A. A.

PY - 2004/3/1

Y1 - 2004/3/1

N2 - We consider quasilinear elliptic non-diagonal systems of equations with strong non-linearity with respect to the gradient. We have already shown that the generalized solution of this problem is Hölder continuous in the neighbourhood of points of the domain at which the norm of the gradient of the solution is sufficiently small in the Morrey space L 2,n-2. We estimate the Hölder norm of the solution in the neighbourhood of such points in terms of its norm in the Sobolev space W 2 1. We obtain a similar result under the Dirichlet boundary condition for points situated in the neighbourhood of the boundary.

AB - We consider quasilinear elliptic non-diagonal systems of equations with strong non-linearity with respect to the gradient. We have already shown that the generalized solution of this problem is Hölder continuous in the neighbourhood of points of the domain at which the norm of the gradient of the solution is sufficiently small in the Morrey space L 2,n-2. We estimate the Hölder norm of the solution in the neighbourhood of such points in terms of its norm in the Sobolev space W 2 1. We obtain a similar result under the Dirichlet boundary condition for points situated in the neighbourhood of the boundary.

UR - http://www.scopus.com/inward/record.url?scp=33746543131&partnerID=8YFLogxK

U2 - 10.1070/IM2004v068n02ABEH000473

DO - 10.1070/IM2004v068n02ABEH000473

M3 - Article

AN - SCOPUS:33746543131

VL - 68

SP - 243

EP - 258

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

SN - 1064-5632

IS - 2

ER -

ID: 15728885