ÇETTORE MAJORANAÈ FOUNDATION AND CENTRE FOR SCIENTIFIC CULTURE TO PAY A PERMANENT TRIBUTE TO GALILEO GALILEI, FOUNDER OF MODERN SCIENCE AND TO ENRICO FERMI, THE “ITALIAN NAVIGATOR”, FATHER OF THE WEAK FORCES

INTERNATIONAL SCHOOL OF ÇGUIDO STAMPACCHIAÈ 58th Workshop: VARIATIONAL ANALYSIS AND APPLICATIONS In memory of M.K.V. Murthy and Guido Stampacchia The Award of the Fourth Gold Medal “Guido Stampacchia”

ERICE-SICILY: 14 – 22 MAY 2012 Sponsored by the: • Italian Ministry of Education, University (PRIN- 2008N4BBLF), and Research • Sicilian Regional Government • Istituto Nazionale di Alta Matematica (GNAMPA) • European Research Council Advanced Grant n.226234 AnTeGeFi • Mediterranea University of Reggio Calabria • University of Catania (Mathematics Dept and Computer Sciences) • University of Messina (Mathematics Dept) PROGRAMME AND LECTURERS Elliptic and Parabolic PDE and Systems with Discontinuous Coefficients ¥ R. HENRION, Weierstrass Institute, Berlin, DE Equilibrium Problems on Networks both in the Static and Dynamic Case ¥ A. IOFFE, Technion Haifa, IL Generalized Complementarity Problems ¥ A.A. KHAN, Rochester Institute of Technology, Rochester, NY, US Hamiltonian Systems Infinite Dimensional Duality Theory ¥ I. LASIECKA, University of Virginia, Charlottesville, VA, US Minimax Problems ¥ M.A. LOPEZ, University of Alicante, ES Minimizers of Free Discontinuity Problems ¥ J.E. MARTINEZ-LEGAZ, University of Barcelona, ES Multifunctions, Differential Inclusions, Optimal Control, Nonconvex Optimization ¥ V. MILLOT, Université Pierre et Marie Curie, , FR Optimization Problems in Mass Transportation Theory ¥ G. MINGIONE, University of Parma, IT Quasidifferential and Subgradients ¥ M. MORINI, University of Parma, IT Set convergence Variational and Quasi-variational Inequalities ¥ B.S. MORDUKHOVICH, Wayne State University, Detroit, MI, US Semicontinuity of Variational Integrals ¥ M. ZUHAIR NASHED, University of Central Florida, Orlando, FL, US Homogenization and Gamma-Convergence ¥ J. OUTRATA, Czech Republic Academy of Science, Prague, CZ Symmetrization and Isoperimetric Inequalities ¥ M. PAPPALARDO, University of Pisa, IT Free Interface Problems ¥ A. PRATELLI, University of Pavia, IT ¥ F. RACITI, University of Catania, IT ¥ A. ARUTYUNOV, Moscow State University, RU ¥ M.A. RAGUSA, University of Catania, IT ¥ A. AUSLENDER, University of Lyon I, Lyon, FR ¥ B. RICCERI, University of Catania, IT ¥ A. BARBAGALLO, University of “Federico II”, IT ¥ S.M. ROBINSON, University of Wisconsin-Madison, WI, US ¥ G. BUTTAZZO, University of Pisa, IT ¥ T. ROCKAFELLAR, University of Washington, Seattle, WA, US ¥ V. CASELLES, Universitat Pompeu Fabra, Barcelona, ES ¥ L. SCRIMALI, University of Catania, IT ¥ G. COLOMBO, University of Padova, IT ¥ M.A. THÉRA, Université de Limoges, FR • B. DACOROGNA, Université de Lausanne, CH ¥ L. THIBAULT, Université de Montpellier, FR ¥ P. DANIELE, University of Catania, IT ¥ R. TRIGGIANI, University of Virginia, Charlottesville, VA, US ¥ V.F. DEMYANOV, St. Petersburg State University, St. Petersburg, RU ¥ E. VALDINOCI, University of Roma "Tor Vergata", , IT ¥ A.L. DONTCHEV, University of Michigan, Ann Arbor, MI, US ¥ P. VILLAGGIO, University of Pisa, IT ¥ I. FRAGALË, Politecnico di Milano, IT ¥ C. VITANZA, University of Messina, IT • S. GIUFFRÈ, “Mediterranea” University of Reggio Calabria, IT • C. ZALINESCU, University “Al. I. Cuza”, Iasi, RO

PURPOSE OF THE WORKSHOP POETIC TOUCH The Workshop aims at presenting the state-of-the-art and current research on According to legend, Erice, son of Venus and Neptune, founded a small town Variational Analysis and its Applications. In the past decades Variational Analysis experienced on top of a mountain (750 metres above sea level) more than three thousand years ago. rapid development and it has become one of the most dynamic area of mathematics that The founder of modern history — i.e. the recording of events in a methodic and chronological bridges both abstract and applied analysis and gives an excellent role in the application of sequence as they really happened without reference to mythical causes — the great mathematics to real world problems. In particular, Variational Analysis encompasses a large Thucydides (~500 B.C.), writing about events connected with the conquest of Troy (1183 area of modern Mathematics, including the classical , the Theories B.C.) said: ÇAfter the fall of Troy some Trojans on their escape from the Achaei arrived of Perturbation and of Approximation, Generalized Differentiability, Set Convergence, in Sicily by boat and as they settled near the border with the Sicanians all together they Variational Inequalities and Partial Differential Equations. A leader researcher in Variational were named Elymi: their towns were Segesta and Erice.È This inspired Virgil to describe Analysis, particularly in the field of Variational Inequalities and Partial Differential Equations, the arrival of the Trojan royal family in Erice and the burial of Anchises, by his son was Guido Stampacchia the founder of Variational Inequalities in the 60's of the last century. Aeneas, on the coast below Erice. Homer (~1000 B.C.), Theocritus (~300 B.C.), Polybius The subsequent years have witnessed an outstanding attention to this theory which covers (~200 B.C.), Virgil (~50 B.C.), Horace (~20 B.C.), and others have celebrated this applications of extreme interest related to mathematical and, more recently, to magnificent spot in Sicily in their poems. During seven centuries (XIII-XIX) the town engineering, statistics, economics, financial networks and generalized complementarity of Erice was under the leadership of a local oligarchy, whose wisdom assured a long problems. Several classical and new theories, such as those of evolutionary projected period of cultural development and economic prosperity which in turn gave rise to the dynamical systems and infinite dimensional duality, as well as research in discretized many churches, monasteries and private palaces which you see today.ÊÊÊÊÊÊÊÊÊÊ computational methods, have received a decisive impulse in order to offer effective solutions In Erice you can admire the Castle of Venus, the Cyclopean Walls (~800 B.C.) to until now unsolved problems. The same Guido Stampacchia, with the collaboration of and the Gothic Cathedral (~1300 A.D.). Erice is at present a mixture of ancient and M.K.V. Murthy, gave outstanding contribution to the regularity theory of solutions to Partial medieval architecture. Other masterpieces of ancient civilization are to be found in the Differential Equations, which have a great impact until now. The outstanding results on neighbourhood: at Motya (Phoenician), Segesta (Elymian), and Selinunte (Greek). On Semicontinuity of variational integrals, homogenization and Gamma-convergence, regularity the Aegadian Islands — theatre of the decisive naval battle of the first Punic War (264- of Elliptic PDE's and Systems, Free Discontinuity Problems, Variational Image Segmentation 241 B.C.) — suggestive neolithic and paleolithic vestiges are still visible: the grottoes Models, Symmetrization and Isoperimetric Inequalities, Free interface problems derive, of Favignana, the carvings and murals of Levanzo. partially, from the contributions by Guido Stampacchia. The Workshop aims to offer a Splendid beaches are to be found at San Vito Lo Capo, Scopello, and Cornino, review of research themes, methods and open problems together with outlines of the new and a wild and rocky coast around Monte Cofano: all at less than one hour’s drive from research trends in all the above topics. Erice.

APPLICATIONS More information about the ÇEttore MajoranaÈ Foundation and Centre for Scientific Culture can be found on the WWW at the following address: Persons wishing to attend the Workshop should apply by e-mail to the Co-Director http://www.ccsem.infn.it of the Workshop: ¥ Professor Antonino MAUGERI Department of Mathematics and Computer Science PLEASE NOTE University of Catania, Viale A. Doria, 6 Ð 95125 CATANIA Tel + 39.095.738 3059 Ð Fax + 39.095.330094 Ð e-mail: [email protected] Participants must arrive on 14 May, not later than 6 pm. They should specify: i) date and place of birth, together with current nationality; Closing Date for Applications: 15 April 2012 ii) affiliation; iii) address, e-mail address.

N. FUSCO Ð A. MAUGERI Ð B.S. MORDUKHOVICH F. GIANNESSI A. ZICHICHI DIRECTORS OF THE WORKSHOP DIRECTOR OF THE SCHOOL EMFCSC PRESIDENT AND DIRECTOR OF THE CENTRE