Polyhedricity of convex sets in sobolev space

Refined Convex Sobolev Inequalities

This paper is devoted to refinements of convex Sobolev inequalities in the case of power law relative entropies: a nonlinear entropy–entropy production relation improves the known inequalities of this type. The corresponding generalized Poincaré type inequalities with weights are derived. Optimal constants are compared to the usual Poincaré constant.

Properties of Typical Bounded Closed Convex Sets in Hilbert Space

Baire category techniques are known to be a powerful tool in the investigation of the convex sets. Their use, which goes back to the fundamental contribution of Klee [17], has permitted to discover several interesting unexpected properties of convex sets (see Gruber [14], Schneider [23], Zamfirescu [25]). A survey of this area of research and additional bibliography can be found in [15, 27]. In...

Singular sets of Sobolev functions

Covering Large Balls with Convex Sets in Spherical Space

If the n-dimensional unit sphere is covered by finitely many spherically convex bodies, then the sum of the inradii of these bodies is at least π. This bound is sharp, and the equality case is characterized. MSC 2000: 52A55, 52C17

Some results on functionally convex sets in real Banach spaces

‎We use of two notions functionally convex (briefly‎, ‎F--convex) and functionally closed (briefly‎, ‎F--closed) in functional analysis and obtain more results‎. ‎We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$‎, ‎then $bigcup_{alphain I}A_{alpha}$ is F--convex‎. ‎Moreover‎, ‎we introduce new definition o...