58th Course: VARIATIONAL ANALYSIS AND APPLICATIONS
The Workshop aims at presenting the state-of-the-art and current research on Variational Analysis
and its Applications. In the past decades Variational Analysis experienced rapid development and it
has become one of the most dynamic area of mathematics that bridges both abstract and applied
analysis and gives an excellent role in the application of mathematics to real world problems.
particular, Variational Analysis encompasses a large area of modern Mathematics, including the
classical Calculus of Variations, the Theories of Perturbation and of Approximation, Generalized
Differentiability, Set Convergence, Variational Inequalities and Partial Differential Equations. A
leader researcher in Variational Analysis, particularly in the field of Variational Inequalities and Partial
Differential Equations, was Guido Stampacchia the founder of Variational Inequalities in the
60's of the last century. The subsequent years have witnessed an outstanding attention to this theory
which covers applications of extreme interest related to mathematical physics and, more recently, to
engineering, statistics, economics, financial networks and generalized complementarity problems.
Several classical and new theories, such as those of evolutionary projected dynamical systems and
infinite dimensional duality, as well as research in discretized computational methods, have received
a decisive impulse in order to offer effective solutions to until now unsolved problems. The
same Guido Stampacchia, with the collaboration of M.K.V. Murthy, gave outstanding contribution
to the regularity theory of solutions to Partial Differential Equations, which have a great impact until
now. The outstanding results on Semicontinuity of variational integrals, homogenization and
Gamma-convergence, regularity of Elliptic PDE's and Systems, Free Discontinuity Problems, Variational
Image Segmentation Models, Symmetrization and Isoperimetric Inequalities, Free interface
problems derive, partially, from the contributions by Guido Stampacchia. The workshop aims to offer
a review of research themes, methods and open problems together with outlines of the new research
trends in all the above topics.