The monotonicity condition and a priori estimates of the Hölder norm for a class of nondiagonal elliptic systems with quadratic nonlinearity

Abstract

The Dirichlet problem for quasilinear elliptic systems of equations with nondiagonal principal matrix and additional terms with strong nonlinearity in the gradient is considered. An a priori condition on the behavior of solutions in a neighborhood of a fixed point is stated, which allows us to estimate locally the Hölder norm of a solution in terms of its energy norm. Owing to the monotonicity inequality proved for one class of such systems, the a priori assumption on the behavior of solutions is reduced to an optimal one while estimating the Hölder norm of the solution. Bibliography: 27 titles.