Generalized bi-quasivariational inequalities for quasi-pseudomonotone type II operators on noncompact sets.
We investigate the minima of functionals of the formwhere is strictly convex. The admissible functions are not necessarily convex and satisfy on , , , is a fixed function on . We show that the minimum is attained by , the convex envelope of .
We investigate the minima of functionals of the form where g is strictly convex. The admissible functions are not necessarily convex and satisfy on [a,b], u(a)=f(a), u(b)=f(b), f is a fixed function on [a,b]. We show that the minimum is attained by , the convex envelope of f.
Significant information about the topology of a bounded domain of a Riemannian manifold is encoded into the properties of the distance, , from the boundary of . We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of , as well as applications to homotopy equivalence.
Let (Ω,μ) be a measure space, E be an arbitrary separable Banach space, be the dual equipped with the weak* topology, and g:Ω × E → ℝ be a Carathéodory function which is Lipschitz continuous on each ball of E for almost all s ∈ Ω. Put . Consider the integral functional G defined on some non--type Banach space X of measurable functions x: Ω → E. We present several general theorems on sufficient conditions under which any element γ ∈ X* of Clarke’s generalized gradient (multivalued C-subgradient)...
Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the value function is described by a conic core, a modification of the earlier concept of convex core. Minimizers...