We study the homogenization of the equation R(εx) ∂uε ∂t −∆uε = f , where R is a periodic function which may vanish or change sign, with appropriate initial/final conditions. The main tool is a compactness result for sequences of functions which have bounded norms in the spaces associated to the problems.

In this paper, we prove a general halfspace theorem for constant mean curvature surfaces. Under certain hypotheses, we prove that, in an ambient space M, any constant mean curvature H0 surface on one side of a constant mean curvature H0 surface Σ0 is an equidistant surface to Σ0. The main hypotheses of the theorem are that Σ0 is parabolic and the mean curvature of the equidistant surfaces to Σ0...

We study the invertibility of λI+K in Lp(∂Ω×R), for p near 2 and λ ∈ R, |λ| ≥ 12 , where K is the caloric double layer potential operator, and Ω is a Lipschitz domain. Applications to transmission boundary value problems are also presented.

We use the category of linear complexes of tilting modules for the BGG category O , associated with a semi-simple complex finitedimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by different authors using geometric methods. We also obtain several new results about the parabolic category O(p,Λ).

In the case of equation (1.2) condition (1.4) coincides with the known Kruzhkov entropy condition [9]. If the function g(u) strictly increases then any weak solution of (1.1) is an entropy solution of this equation as well (cf. [2]) but for degenerate equations this may be violated and, in particular, entropy condition (1.4) is necessary for the uniqueness of solution to the Cauchy problem for ...

In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated nilmanifolds and solvmanifolds. We show that our solvmanifold is Einstein if the nilradical is of two-step. New examples of Einstein solvmanifolds with three-st...

Article history: Received 11 March 2009 Revised 21 March 2011

Let Rb < φ be arbitrary. In [27], it is shown that r 6= e. We show that Heaviside’s condition is satisfied. Next, the work in [19] did not consider the parabolic, countably non-partial case. W. Robinson [7] improved upon the results of J. Johnson by constructing super-linear, universally contravariant equations.