# New a priori estimates for nondiagonal strongly nonlinear parabolic systems

Banach Center Publications (2008)

- Volume: 81, Issue: 1, page 13-30
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topArina Arkhipova. "New a priori estimates for nondiagonal strongly nonlinear parabolic systems." Banach Center Publications 81.1 (2008): 13-30. <http://eudml.org/doc/282382>.

@article{ArinaArkhipova2008,

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 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).},

author = {Arina Arkhipova},

journal = {Banach Center Publications},

keywords = {Campanato spaces; partial regularity; quadratic growth in the gradient; quasireverse Hölder inequalities},

language = {eng},

number = {1},

pages = {13-30},

title = {New a priori estimates for nondiagonal strongly nonlinear parabolic systems},

url = {http://eudml.org/doc/282382},

volume = {81},

year = {2008},

}

TY - JOUR

AU - Arina Arkhipova

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

JO - Banach Center Publications

PY - 2008

VL - 81

IS - 1

SP - 13

EP - 30

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).

LA - eng

KW - Campanato spaces; partial regularity; quadratic growth in the gradient; quasireverse Hölder inequalities

UR - http://eudml.org/doc/282382

ER -

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.