On Lipschitz continuity of the solution map for two-dimensional wave maps
On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
We study properties of Lipschitz truncations of Sobolev functions with constant and variable exponent. As non-trivial applications we use the Lipschitz truncations to provide a simplified proof of an existence result for incompressible power-law like fluids presented in [Frehse et al., SIAM J. Math. Anal34 (2003) 1064–1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.
On local and global analytic and Gevrey hypoellipticity
On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion
The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the -approach the Lagrangian coordinates must be used. We are looking...
On local Lipschitz continuity of superposition operators
On local motion of a compressible barotropic viscous fluid bounded by a free surface
We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the existence time....
On local motion of a general compressible viscous heat conducting fluid bounded by a free surface
The motion of a viscous compressible heat conducting fluid in a domain in ℝ³ bounded by a free surface is considered. We prove local existence and uniqueness of solutions in Sobolev-Slobodetskiĭ spaces in two cases: with surface tension and without it.
On local properties of some classes of infinitely degenerate elliptic differential operators.
On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids
The local existence of solutions for the compressible Navier-Stokes equations with the Dirichlet boundary conditions in the -framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the -approach, because the velocity belongs to with r > 3.
On localization of solutions of elliptic equations with nonhomogeneous anisotropic degeneracy.
On long time behaviour of a class of reaction-diffusion models
On lower-semicontinuity of variational integrals
On Lp estimates for square roots of second order elliptic operators on Rn.
On Lp - Lp' Estimates for the Wave Equation.
On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.
On -accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry.
On M. Kac's probabilistic formula for the solution of the telegraphist's equation
On -sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry
We consider a Schrödinger-type differential expression , where is a -bounded Hermitian connection on a Hermitian vector bundle of bounded geometry over a manifold of bounded geometry with metric and positive -bounded measure , and is a locally integrable section of the bundle of endomorphisms of . We give a sufficient condition for -sectoriality of a realization of in . In the proof we use generalized Kato’s inequality as well as a result on the positivity of satisfying the...
On Maximal Functions and Parabolic Limits.
On maximum principle for weak subsolutions of degenerate parabolic linear equations
Sufficient conditions are obtained so that a weak subsolution of , bounded from above on the parabolic boundary of the cylinder , turns out to be bounded from above in .