[Author]
A. A. Arkhipova
[Title]
New a priori estimates for nondiagonal strongly nonlinear parabolic systems
[AMS Subj-class]
35K45 Initial value problems for parabolic systems
35K50 Boundary value problems for parabolic systems
35K55 Nonlinear PDE of parabolic type
35B65 Smoothness and regularity of solutions of PDE
35A20 Analytic methods, singularities
[Abstract]
We consider elliptic and parabolic systems of equations with
quadratic nonlinearities in the gradient. We discuss new
description of regular points of solutions of such type systems.
For a class of strongly nonlinear parabolic systems, we estimate
locally the Holder norm of a solution. Instead of smallness of the
osscillation, we assume local smallness of the Campanato seminorm of
the solution under consideration. Theorems about quasireverse
Holder inequalities proved by the author are essentially used. We
study systems under the Dirichlet boundary condition and estimate
the Holder norm of a solution up to the boundary (up to the
parabolic boundary of the prescribed cylinder in the parabolic
case).
[Keywords]
parabolic systems, strong nonlinearity, regularity
[Comments]
English, LaTeX, 25 pp.
[Contact e-mail]
arina@AA1101.spb.edu