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New a priori estimates for nondiagonal strongly nonlinear parabolic systems

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Arkhipova A.

Banach Center Publications

2008

tom 81

nr 1

13-30

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).

Ograniczanie wyników

1 Banach Center Publications

1 Arkhipova A.

1 2008

Wyniki wyszukiwania

New a priori estimates for nondiagonal strongly nonlinear parabolic systems