Advances in Mathematical Economics: Volume 23

Editor's Preface
Contents
Evolution Problems with Time-Dependent Subdifferential Operators
	1 Introduction
	2 Notation and Preliminaries
	3 Results with Single-Valued Time-Dependent Perturbation
	4 Extension to L2H([0, T]) of Subdifferential Operator ∂φ(t, ·)
	5 Main Results
		5.1 Existence Results for Problem (P2)
		5.2 Some Variants with the Velocity in the Subdifferential
	6 Applications
		6.1 A Skorokhod Problem
		6.2 Towards a Couple of Evolution Inclusion Involving Fractional Differential Equation
		6.3 A Second Order Evolution Inclusion
	References
Infinite Horizon Optimal Control of Non-Convex Problems Under State Constraints
	1 Introduction
	2 Preliminaries and Notations
	3 Value Function of the Infinite Horizon Problem
	4 Upper Semicontinuity of the Value Function
	5 Relaxation in the Absence of State Constraints
	6 Relaxation in the Presence of State Constraints
	7 Relation to a Finite Horizon Bolza Problem
	8 Maximum Principle and Sensitivity Relation
	9 Hamilton–Jacobi Equation
	References
The Nonemptiness of the Inner Core
	1 Introduction
	2 NTU Games and the Inner Core
	3 Characterization of Efficient Surface with Strictly Positive Normal Vectors
	4 Nonemptiness of the Inner Core
	5 NTU Games Generated by Exchange Economies
	6 Concluding Remarks
	References
Complicated Dynamics and Parametric Restrictions in the Robinson-Solow-Srinivasan (RSS) Model
	1 Introduction
	2 The Two-Sector RSS Model
		2.1 Constructs from Dynamic Programming
		2.2 The Modified Golden Rule
		2.3 A Failure of Strict Concavity
		2.4 Basic Properties of the OPC
	3 An Explicit Solution of the OPF
	4 Optimal Topological Chaos
	5 Technological Restrictions for Optimal Topological Chaos
		5.1 Technological Restrictions for Optimal Period-Three Cycles
		5.2 Technological Restrictions for Optimal Turbulence
	6 Discount-Factor Restrictions for Optimal Topological Chaos
		6.1 Discount-Factor Restrictions for Optimal Period-Three Cycles
		6.2 Discount-Factor Restrictions for Optimal Turbulence
	7 Concluding Remarks
	Appendix
		Lemmata for the Proof of Proposition 7
		Lemmata for the Proof of Proposition 8(ii)
			A Monotone Property
			A Straight-Down-the-Turnpike Property
		An OPF for a Special Case
		Proof of Proposition 8(ii)
	References
Some Regularity Estimates for Diffusion Semigroups with Dirichlet Boundary Conditions
	1 Introduction
	2 Part I: Horizontal Direction
		2.1 Normed Spaces and Interpolation
		2.2 Basic Results
		2.3 Main Lemma
		2.4 Proof of Theorem 3(1)
		2.5 Dual Operators
	3 Part II: Vertical Direction
		3.1 Banach Spaces
		3.2 Some Normed Spaces
		3.3 Differential Operators and Basic Equality
		3.4 L∞-Estimate
		3.5 L1-Estimate
		3.6 Proof of Theorem 2
	References
Disintegration of Young Measures and Nonlinear Analysis
	1 Introduction
	2 Disintegrations
		2.1 Measurable Family of Measures
		2.2 The Dual of L1(Ω, C∞(X, R))
		2.3 Disintegration Theorem (A)
		2.4 Auxiliary Preparations
		2.5 Disintegration Theorem (B)
		2.6 Conditional Probabilities
	3 Convergence
		3.1 Narrow Topology
		3.2 Convergence of Young Measures Associated with Measurable Functions
		3.3 Tightness
		3.4 Multiple Young Measures
		3.5 Simple Variational Problems via Theory of Young Measures
	4 Continuity of Nonlinear Integral functionals
		4.1 Roles of Uniform Integrability
		4.2 Castaing–Clauzure Theorem
		4.3 Towards Calculus of Variations
	References
Complete List of Works Published in Advances in Mathematical Economics Vol. 1–23
Index