New a priori estimates for nondiagonal strongly nonlinear parabolic systems

• Autorzy: Arina Arkhipova
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 35J60: Nonlinear elliptic equations
• 35B45: A priori estimates
• 35K40: Second-order parabolic systems
• 35B65: Smoothness and regularity of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 13-30

Daty

wydano

2008

Twórcy

autor

Arina Arkhipova

• Mathematics and Mechanics Department, St-Petersburg State University, Universitetskaya ul., 28, Stary Petergof, 198504, St-Petersburg, Russia

Identyfikatory

DOI

10.4064/bc81-0-1