International Workshop

PURPOSE OF THE WORKSHOP “VARIATIONAL ANALYSIS AND APPLICATIONS”

The workshop aims at presenting state-of-the-art and current research directions in variational analysis and partial differential equations and systems.

Variational analysis encompasses a large area of modern mathematics, including the classic calculus of variations, the theories of perturbation, approximation, subgradient, subderivatives, set convergence and variational inequalities. Originating with the Signorini problem, about 5 decades ago, variational inequalities have undergone great development and influence both in the progress of variational analysis, and in applications to mathematical physics and, more recently, to engineering, statistics, economics, financial networks and generalized complementarity problems.

In particular, several classical and new theories have received a strong impulse for effective solutions to until-now unsolved problems. These theories include: infinite dimensional duality and zero duality gap, minimax problems, variational principles and fixed points problems, Jacobian and Hessian equations, degenerate problems,  variational problems with measurable coefficients, inverse variational problems, second order optimality conditions, infima over sub-level sets, stochastic variational inequalities and optimization problems, variational and differential inclusions.

The workshop aims at offering a review of the results achieved in the above research themes, specifying the used methods and pointing out the open problems together with outlines of the new research trends in the principal topics of variational analysis and applications.

The sessions of September 3-4 will be dedicated to Professor Antonino Maugeri in the occasion of his 70th birthday.

The proceedings of the special session dedicated to Professor Maugeri, but extended also to all the participants in the international workshop, will be published in a special issue of Journal of Convex Analysis, edited by P. Daniele, F. Giannessi and M. Théra. The deadline for submitting the contribution is November 1, 2015.

During the opening ceremony of the International Workshop, a Gold Medal in honour of Guido Stampacchia will be assigned for the fifth time, after an international competition, to a young mathematician, whose age be not greater than 35 years at the date of December 31st 2015, for his scientific contribution in the field of Variational Analysis.

GOLD MEDAL GUIDO STAMPACCHIA

Fifth edition of the Gold Medal «Guido Stampacchia» Prize
The Stampacchia Gold Medal is an international award to mathematicians who have not passed the age of 35. The award is given in recognition of studies in the field of the calculus of variations and its applications that have had a strong impact and international recognition. The medal is named in memory of the Italian mathematician Guido Stampacchia (Naples, March 26, 1922 – Paris, April 27, 1978).
The award is sponsored jointly by the Unione Matematica Italiana (UMI) and the Ettore Majorana Foundation and Centre for Scientific Culture (Erice) and is awarded by an international commission composed of eminent mathematicians. Such a committee is appointed by UMI. The award ceremony takes place during the opening ceremony of the International Conference on Variational Analysis and Applications that is organized every three years at the School of Mathematics “Guido Stampacchia” of the Foundation “Ettore Majorana”.

For additional details go to Gold Medal «Guido Stampacchia» Prize

TOPICS

    • Evolutionary Projected Dynamical Systems
    • Infinite Dimensional Duality
    • Minimax Problems
    • Existence of Solutions for Jacobian and Hessian Equations
    • Optimal Control
    • Differential Inclusions
    • Dual Conditions for Nonconvex Functions
    • Moving Boundary Variational Problems
    • Inverse Variational Inequalities
    • Degenerate Transmission Problems
    • Obstacle Problems with Measurable Coefficients
    • Second Order Optimality Conditions
    • Infima over Sub-Level Sets
    • Relaxation Methods in Hilbert Spaces
    • New Energy Inversion in Saddle Point Problems
    • Stochastic Variational Inequalities

POETIC TOUCH

According to legend, Erice, son of Venus and Neptune, founded a small town on top of a mountain (750 metres above sea level) more than three thousand years ago. The founder of modern history – i.e. the recording of events in a methodic and chronological sequence as they really happened without reference to mythical causes – the great Thucydides ( ~500 B.C.), writing about events connected with the conquest of Troy (1183 B.C.) said: «After the fall of Troy some Trojans on their escape from the Achaei arrived in Sicily by boat and as they settled near the border with Sicanians all together they were named Elymi: their towns were Segesta and Erice.» This inspired Virgil to describe the arrival of the Trojan royal family in Erice and the burial of Anchise, by his son Enea, on the cost below Erice. Homer ( ~1000 B.C.), Theocritus ( ~300 B.C.), Plybius ( ~200 B.C.), Virgil ( ~50 B.C.), Horace ( ~20 B.C.), and others have celebrated this magnificent spot in Sicily in their poems. During seven centuries (XIII-XIX) the town of Erice was under the leadership of a local oligarchy, whose wisdom assured a long period of cultural development and economic prosperity which in turn gave rise to the many churches, monasteries and private palaces which you see today.
In Erice you can admire the Castle of Venus, the Cyclopean Walls ( ~800 B.C.)and the Gothic Cathedral ( ~1300 A.D.). Erice is at present a mixture of ancient and medieval architecture. Other masterpieces of ancient civilization are to be found in the neighbourhood: at Motya (Phoenician), Segesta (Elymian), and Selinunte (Greek). On the Aegadian Islands – theatre of the decisive naval battle of the first Punic War (264-241 B.C.) – suggestive neolithic and paleolithic vestiges are still visible: the grottoes of Favignana, the carvings and murals of Levanzo.
Splendid beaches are to be found at San Vito Lo Capo, Scopello, and Cornino, and a wild and rocky coast around Monte Cofano: all at less than one hour’s drive from Erice.

DIRECTORS

Patrizia DANIELE, University of Catania (daniele@dmi.unict.it)

Camillo DE LELLIS, University of Zurich (camillo.delellis@math.uzh.ch)

Antonino MAUGERI, University of Catania (maugeri@dmi.unict.it)

Tyrrell R. ROCKAFELLAR, University of Washington (rtr@math.washington.edu)

Michel THÉRA, University of Limoges (michel.thera@unilim.fr)