Variational Analysis and Applications

J. -L. Lions (auth.), Franco Giannessi, Antonino Maugeri (eds.)9780387242095, 0387242090

This book discusses a new discipline, variational analysis, which contains the calculus of variations, differential calculus, optimization, and variational inequalities. To such classic branches of mathematics, variational analysis provides a uniform theoretical base that represents a powerful tool for the applications. The contributors are among the best experts in the field.

Audience

The target audience of this book includes scholars in mathematics (especially those in mathematical analysis), mathematical physics and applied mathematics, calculus of variations, optimization and operations research, industrial mathematics, structural engineering, and statistics and economics.

Table of contents :
Front Matter….Pages 1-1
The Work of G. Stampacchia in Variational Inequalities….Pages 3-30
In Memory of Guido Stampacchia….Pages 31-32
The Collaboration between Guido Stampacchia and Jacques-Louis Lions on Variational Inequalities….Pages 33-38
In Memory of Guido Stampacchia….Pages 39-46
Guido Stampacchia….Pages 47-77
Memories of Guido Stampacchia….Pages 79-80
In Memory of Guido Stampacchia….Pages 81-82
Guido Stampacchia, My Father….Pages 83-86
Front Matter….Pages 87-87
Convergence and Stability of a Regularization Method for Maximal Monotone Inclusions and Its Applications to Convex Optimization….Pages 89-132
Partitionable Mixed Variational Inequalities….Pages 133-146
Irreducibility of the Transition Semigroup Associated with the Two Phase Stefan Problem….Pages 147-159
On Some Boundary Value Problems for Flows with Shear Dependent Viscosity….Pages 161-172
Homogenization of Systems of Partial Differential Equations….Pages 173-193
About the Duality Gap in Vector Optimization….Pages 195-204
Separation of Convex Cones and Extremal Problems….Pages 205-213
Infinitely Many Solutions for the Dirichlet Problem Via a Variational Principle of Ricceri….Pages 215-229
A Density Result on the Space VMO ω ….Pages 231-237
Linear Complementarity Since 1978….Pages 239-257
Variational Inequalities in Vector Optimization….Pages 259-278
Variational Inequalities for General Evolutionary Financial Equilibrium….Pages 279-299
Front Matter….Pages 87-87
Variational Control Problems with Constraints Via Exact Penalization….Pages 301-342
Continuous Sets and Non-Attaining Fuctionals in Reflexive Banach Spaces….Pages 343-357
Existence and Multiplicity Results for a Non Linear Hammerstein Integral Equation….Pages 359-371
Differentiability of Weak Solutions of Nonlinear Second Order Parabolic Systems with Quadratic Growth and Non Linearity q ≥ 2….Pages 373-392
An Optimization Problem with an Equilibrium Constraint in Urban Transport….Pages 393-408
Sharp Estimates for Green’s Functions: Singular Cases….Pages 409-426
First-Order Conditions for C 0,1 Constrained Vector Optimization….Pages 427-450
Global Regularity for Solutions to Dirichlet Problem for Elliptic Systems with Nonlinearity q ≥ 2 and with Natural Growth….Pages 451-463
Optimality Conditions for Generalized Complementarity Problems….Pages 465-475
Variational Inequalities for Time Dependent Financial Equilibrium with Price Constraints….Pages 477-496
Remarks About Diffusion Mediated Transport: Thinking About Motion in Small Systems….Pages 497-511
Augmented Lagrangian and Nonlinear Semidefinite Programs….Pages 513-529
Optimality Alternative: a Non-Variational Approach to Necessary Conditions….Pages 531-552
A Variational Inequality Scheme for Determining an Economic Equilibrium of Classical or Extended Type….Pages 553-577
On Time Dependent Vector Equilibrium Problems….Pages 579-587
On Some Nonstandard Dynamic Programming Problems of Control Theory….Pages 589-603
Properties of Gap Function for Vector Variational Inequality….Pages 605-631
Zero Gravity Capillary Surfaces and Integral Estimates….Pages 633-649
Asymptotically Critical Points and Multiple Solutions in the Elastic Bounce Problem….Pages 651-663
A Branch-and-Cut to the Point-to-Point Connection Problem on Multicast Networks….Pages 665-680
Front Matter….Pages 87-87
Variational Inequality and Evolutionary Market Disequilibria: The Case of Quantity Formulation….Pages 681-696
Numerical Approximation of Free Boundary Problem by Variational Inequalities. Application to Semiconductor Devices….Pages 697-722
Sensitivity Analysis for Variational Systems….Pages 723-743
Stable Critical Points for the Ginzburg Landau Functional on Some Plane Domains….Pages 745-764
The Distance Function to the Boundary and Singular Set of Viscosity Solutions of Hamilton-Jacobi Equation….Pages 765-772
L P -Regularity for Poincaré Problem and Applications….Pages 773-789
Minimal Fractions of Compact Convex Sets….Pages 791-811
On Generalized Variational Inequalities….Pages 813-826
Bounded (Hausdorff) Convergence: Basic Facts and Applications….Pages 827-854
Control Processes with Distributed Parameters in Unbounded Sets. Approximate Controllability with Variable Initial Locus….Pages 855-887
Well Posedness and Optimization Problems….Pages 889-904
Semismooth Newton Methods for Shape-Preserving Interpolation, Option Price and Semi-Infinite Programs….Pages 905-919
Hölder Regularity Results for Solutions of Parabolic Equations….Pages 921-934
Survey on the Fenchel Problem of Level Sets….Pages 935-951
Integral Functionals on Sobolev Spaces Having Multiple Local Minima….Pages 953-961
Aspects of the Projector on Prox-Regular Sets….Pages 963-973
Application of Optimal Control Theory to Dynamic Soaring of Seabirds….Pages 975-994
On the Convergence of the Matrices Associated to the Adjugate Jacobians….Pages 995-1006
Quasi-Variatonal Inequalities Applied to Retarded Equilibria in Time-Dependent Traffic Problems….Pages 1007-1023
Higher Order Approximation Equations for the Primitive Equations of the Ocean….Pages 1025-1048
Front Matter….Pages 87-87
Hahn-Banach Theorems and Maximal Monotonicity….Pages 1049-1083
Concrete Problems and the General Theory of Extremum….Pages 1085-1100
Numerical Solution for Pseudomonotone Variational Inequality Problems by Extragradient Methods….Pages 1101-1128
Regularity and Existence Results for Degenerate Elliptic Operators….Pages 1129-1140
Vector Variational Inequalities and Dynamic Traffic Equilibria….Pages 1141-1157
A New Proof of the Maximal Monotonicity of the Sum Using the Fitzpatrick Function….Pages 1159-1172