Regularity results for non-linear elliptic systems in two dimensions
Some (new) counterexamples of parabolic systems
We give examples of parabolic systems (in space dimension ) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.
On the behaviour of solutions to the nonlinear elliptic Neumann problem in unbounded domains
The asymptotic behaviour is studied for minima of regular variational problems with Neumann boundary conditions on noncompact part of boundary.
On the regularity of the weak solution of Cauchy problem for nonlinear parabolic systems via Liouville property
Zemřel Rudolf Švarc
O 19. a 20. Hilbertově problému
A priori estimates for quasilinear parabolic systems with quadratic nonlinearities in the gradient
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.
O jednom jubilantovi
On existence and regularity of solutions to a class of generalized stationary Stokes problem
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 is replaced by a linear operator of first order.
Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices
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 -caloric approximation method. The method was applied by the authors earlier to study regularity of quasilinear systems.
Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem
We prove the existence of regular solution to a system of nonlinear equations describing the steady motions of a certain class of non-Newtonian fluids in two dimensions. The equations are completed by requirement that all functions are periodic.
Counterexample to the regularity of weak solution of elliptic systems
A note on the regularity of autonomous quasilinear elliptic and parabolic systems
Liouville type condition and the interior regularity of quasilinear parabolic system (the case of BMO-solutions)
Nowhere continuous solutions to elliptic systems
Nowhere continuous solutions to elliptic systems
Counterexample to the regularity of weak solution of the quasilinear parabolic system
An anniversary. [Jindřich Nečas]
Gas exhalation and its calculations. I
Some regularity results for quasilinear parabolic systems
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