We extend the notion of quasibounded harmonic functions to plurisubharmonic setting. As an application, using theory Jensen measures, we show that certain generalized Dirichlet problems with unbounded boundary data admit unique solutions, and these solutions are continuous outside a pluripolar set.

We give sufficient conditions under which solutions of discretized in space second-order parabolic and elliptic equations, perhaps degenerate, admit estimates of the first derivatives in the space variables independent of the mesh size.

By means of Ryan’s necessary condition and of some examples, we see how the interpretation of solutions of systems with discontinuous righthand side influences stabilizability results for systems which do not admit continuous stabilizing feedback laws.

We show that there exist maximal globally hyperbolic solutions of the Einstein-dust equations which admit a constant mean curvature Cauchy surface, but are not covered by a constant mean curvature foliation.

Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and quadratic in momenta. In the Euler angle variables (θ, φ, ψ) these integrals give separation equa...

In classical continuum mechanics, quasi-linear systems of conservation laws can be symmetrized if they admit an additional convex conservation law. In particular, this implies the hyperbolicity of governing equations. For capillary fluids, the internal energy depends not only on the density but also on its derivatives with respect to space variables. Consequently, the governing equations belong...

This paper is concerned with the logical structure of arithmetical the ories We survey results concerning logics and admissible rules of con structive arithmetical theories We prove a new theorem the admissible propositional rules of Heyting Arithmetic are the same as the admissible propositional rules of Intuitionistic Propositional Logic We provide some further insights concerning predicate l...

Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field theories, classical topological field theories – whose classical solutions span topological classes of manifolds – and reparametri-sation invariant theories – gener...

J. Dynamics and Diff. Eqns., in press, 2004. The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier-Stokes equations....