[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