Sufficient conditions for the existence and Lipschitz continuity of optimal strategies for static team optimization problems are studied. Revised statements and proofs of some results in “Kim K.H., Roush F.W., Team Theory. Ellis Horwood Limited Publishers, Chichester, UK, 1987” are presented. Keywords—Statistical information structure, team utility function, value of a team, Lipschitz continuity.

This article is concerned with symmetry properties of the solutions of the reaction-diiusion equation u + f (u) = 0 in a bounded connected domain in R N (N = 2; 3; : : :). Of especial interest are nonlinear source terms f of the type f (u) = u p ? u q with 0 q < p 1. Two results are presented. The rst result concerns the solution of a free boundary problem, where the domain is unknown and u and...

Let (M, d(x, y)) be a metric space. Thus M is a nonempty set and d(x, y) is a nonnegative real-valued function defined for x, y ∈ M such that d(x, y) = 0 if and only if x = y, d(y, x) = d(x, y) for all x, y ∈ M , and d(x, z) ≤ d(x, y) + d(y, z) (1) for all x, y, z ∈ M. If d(x, z) ≤ max(d(x, y), d(y, z)) (2) for all x, y, z ∈ M , then we say that d(x, y) defines an ultrametric on M. A real-value...

Theorem A. Let g : [0, T ]× IR 7→ IR be a bounded function. (i) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is continuous for each t, then the Cauchy problem (1.1) has at least one solution. (ii) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is Lipschitz continuous for each t, with a uniform Lipschitz constant, then the Cauchy problem (1...

Let E be a closed set in R, and suppose that there is a k ≥ 1 such that every x, y ∈ E can be connected by a rectifiable path in E with length ≤ k |x−y|. This condition is satisfied by chord-arc curves, Lipschitz manifolds of any dimension, and fractals like Sierpinski gaskets and carpets. Note that length-minimizing paths in E are chord-arc curves with constant k. A basic feature of this condi...