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A priori estimates for quasilinear parabolic systems with quadratic nonlinearities in the gradient

Arina A. ArkhipovaJana Stará — 2010

Commentationes Mathematicae Universitatis Carolinae

We derive local a priori estimates of the Hölder norm of solutions to quasilinear elliptic systems with quadratic nonlinearities in the gradient. We assume higher integrability of solutions and smallness of its BMO norm but the Hölder norm is estimated in terms of BMO norm of the solution under consideration, only.

Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices

Arina A. ArkhipovaJana Stará — 2019

Commentationes Mathematicae Universitatis Carolinae

Partial regularity of solutions to a class of second order nonlinear parabolic systems with non-smooth in time principal matrices is proved in the paper. The coefficients are assumed to be measurable and bounded in the time variable and VMO-smooth in the space variables uniformly with respect to time. To prove the result, we apply the so-called A ( t ) -caloric approximation method. The method was applied by the authors earlier to study regularity of quasilinear systems.

On existence and regularity of solutions to a class of generalized stationary Stokes problem

Nguyen Duc HuyJana Stará — 2006

Commentationes Mathematicae Universitatis Carolinae

We investigate the existence of weak solutions and their smoothness properties for a generalized Stokes problem. The generalization is twofold: the Laplace operator is replaced by a general second order linear elliptic operator in divergence form and the “pressure” gradient p is replaced by a linear operator of first order.

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