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.
Résumé
This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics "G.Stampacchia" of the "E.Majorana" Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.
Contenu
1.- The Work of G. Stampacchia in Variational Inequalities.- In Memory of Guido Stampacchia.- The Collaboration between Guido Stampacchia and Jacques-Louis Lions on Variational Inequalities.- In Memory of Guido Stampacchia.- Guido Stampacchia.- Memories of Guido Stampacchia.- In Memory of Guido Stampacchia.- Guido Stampacchia, My Father.- 2.- Convergence and Stability of a Regularization Method for Maximal Monotone Inclusions and Its Applications to Convex Optimization.- Partitionable Mixed Variational Inequalities.- Irreducibility of the Transition Semigroup Associated with the Two Phase Stefan Problem.- On Some Boundary Value Problems for Flows with Shear Dependent Viscosity.- Homogenization of Systems of Partial Differential Equations.- About the Duality Gap in Vector Optimization.- Separation of Convex Cones and Extremal Problems.- Infinitely Many Solutions for the Dirichlet Problem Via a Variational Principle of Ricceri.- A Density Result on the Space VMO ?.- Linear Complementarity Since 1978.- Variational Inequalities in Vector Optimization.- Variational Inequalities for General Evolutionary Financial Equilibrium.- Variational Control Problems with Constraints Via Exact Penalization.- Continuous Sets and Non-Attaining Fuctionals in Reflexive Banach Spaces.- Existence and Multiplicity Results for a Non Linear Hammerstein Integral Equation.- Differentiability of Weak Solutions of Nonlinear Second Order Parabolic Systems with Quadratic Growth and Non Linearity q ? 2.- An Optimization Problem with an Equilibrium Constraint in Urban Transport.- Sharp Estimates for Green's Functions: Singular Cases.- First-Order Conditions for C 0,1 Constrained Vector Optimization.- Global Regularity for Solutions to Dirichlet Problem for Elliptic Systems with Nonlinearity q ? 2and with Natural Growth.- Optimality Conditions for Generalized Complementarity Problems.- Variational Inequalities for Time Dependent Financial Equilibrium with Price Constraints.- Remarks About Diffusion Mediated Transport: Thinking About Motion in Small Systems.- Augmented Lagrangian and Nonlinear Semidefinite Programs.- Optimality Alternative: a Non-Variational Approach to Necessary Conditions.- A Variational Inequality Scheme for Determining an Economic Equilibrium of Classical or Extended Type.- On Time Dependent Vector Equilibrium Problems.- On Some Nonstandard Dynamic Programming Problems of Control Theory.- Properties of Gap Function for Vector Variational Inequality.- Zero Gravity Capillary Surfaces and Integral Estimates.- Asymptotically Critical Points and Multiple Solutions in the Elastic Bounce Problem.- A Branch-and-Cut to the Point-to-Point Connection Problem on Multicast Networks.- Variational Inequality and Evolutionary Market Disequilibria: The Case of Quantity Formulation.- Numerical Approximation of Free Boundary Problem by Variational Inequalities. Application to Semiconductor Devices.- Sensitivity Analysis for Variational Systems.- Stable Critical Points for the Ginzburg Landau Functional on Some Plane Domains.- The Distance Function to the Boundary and Singular Set of Viscosity Solutions of Hamilton-Jacobi Equation.- L P-Regularity for Poincaré Problem and Applications.- Minimal Fractions of Compact Convex Sets.- On Generalized Variational Inequalities.- Bounded (Hausdorff) Convergence: Basic Facts and Applications.- Control Processes with Distributed Parameters in Unbounded Sets. Approximate Controllability with Variable Initial Locus.- Well Posedness and Optimization Problems.- Semismooth Newton Methods for Shape-Preserving Interpolation,Option Price and Semi-Infinite Programs.- Hölder Regularity Results for Solutions of Parabolic Equations.- Survey on the Fenchel Problem of Level Sets.- Integral Functionals on Sobolev Spaces Having Multiple Local Minima.- Aspects of the Projector on Prox-Regular Sets.- Application of Optimal Control Theory to Dynamic Soaring of Seabirds.- On the Convergence of the Matrices Associated to the Adjugate Jacobians.- Quasi-Variatonal Inequalities Applied to Retarded Equilibria in Time-Dependent Traffic Problems.- Higher Order Approximation Equations for the Primitive Equations of the Ocean.- Hahn-Banach Theorems and Maximal Monotonicity.- Concrete Problems and the General Theory of Extremum.- Numerical Solution for Pseudomonotone Variational Inequality Problems by Extragradient Methods.- Regularity and Existence Results for Degenerate Elliptic Operators.- Vector Variational Inequalities and Dynamic Traffic Equilibria.- A New Proof of the Maximal Monotonicity of the Sum Using the Fitzpatrick Function.