We extend the property (N) introduced by Jameson for closed convex cones to the normal property for a nite collection of convex sets in a Hilbert space. Variations of the normal property, such as the weak normal property and the uniform normal property, are also introduced. A dual form of the normal property is derived. When applied to closed convex cones, the dual normal property is the proper...

Abstract In this paper, we analyze some properties of a sixth-order elliptic operator arising in the framework strain gradient linear elasticity theory for nanoplates flexural deformation. We first rigorously deduce weak formulation underlying Neumann problem as well its posedness. Under suitable smoothness assumptions on coefficients and geometry, derive interior boundary regularity estimates ...

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck/ log∗ k pairs of parts which are not -regular, where c, > 0 are absolute constants. This bound is tight up to the constant c and addresses a question of Gowers on the number of irregular pairs in Szemerédi’s regularity lemma. In order to gain some control ...