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New a priori estimates for nondiagonal strongly nonlinear parabolic systems. / Arkhipova, A.

In: Banach Center Publications, Vol. 81, 2008, p. 13-30.

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

Harvard

Arkhipova, A 2008, 'New a priori estimates for nondiagonal strongly nonlinear parabolic systems', Banach Center Publications, vol. 81, pp. 13-30. https://doi.org/doi:10.4064/bc81-0-1

APA

Arkhipova, A. (2008). New a priori estimates for nondiagonal strongly nonlinear parabolic systems. Banach Center Publications, 81, 13-30. https://doi.org/doi:10.4064/bc81-0-1

Vancouver

Arkhipova A. New a priori estimates for nondiagonal strongly nonlinear parabolic systems. Banach Center Publications. 2008;81:13-30. https://doi.org/doi:10.4064/bc81-0-1

Author

Arkhipova, A. / New a priori estimates for nondiagonal strongly nonlinear parabolic systems. In: Banach Center Publications. 2008 ; Vol. 81. pp. 13-30.

BibTeX

@article{451fcf8eb9914398a05e672da9f93163,
title = "New a priori estimates for nondiagonal strongly nonlinear parabolic systems",
abstract = "We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the H{\"o}lder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse H{\"o}lder inequalities proved by the author are essentially used. We study systems under the Dirichlet boundary condition and estimate the H{\"o}lder norm of a solution up to the boundary (up to the parabolic boundary of the prescribed cylinder in the parabolic case).",
author = "A. Arkhipova",
year = "2008",
doi = "doi:10.4064/bc81-0-1",
language = "English",
volume = "81",
pages = "13--30",
journal = "Banach Center Publications",
issn = "0137-6934",
publisher = "Polish Academy of Sciences Publishing House",

}

RIS

TY - JOUR

T1 - New a priori estimates for nondiagonal strongly nonlinear parabolic systems

AU - Arkhipova, A.

PY - 2008

Y1 - 2008

N2 - We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the author are essentially used. We study systems under the Dirichlet boundary condition and estimate the Hölder norm of a solution up to the boundary (up to the parabolic boundary of the prescribed cylinder in the parabolic case).

AB - We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the author are essentially used. We study systems under the Dirichlet boundary condition and estimate the Hölder norm of a solution up to the boundary (up to the parabolic boundary of the prescribed cylinder in the parabolic case).

U2 - doi:10.4064/bc81-0-1

DO - doi:10.4064/bc81-0-1

M3 - Article

VL - 81

SP - 13

EP - 30

JO - Banach Center Publications

JF - Banach Center Publications

SN - 0137-6934

ER -

ID: 107751110