### Théorie des équations aux dérivées partielles

##### Luigi Ambrosio

**The theory of partial differential equations**is a fascinating subject of modern mathematics with numerous applications in ranging from

**physics to economics**, from fluid dynamics to meteorology. Prof. Ambrosio revolutionized this area of mathematics by introducing several novel concepts and solving long-standing open problems in this research area. Due to his results, we have today a much better understanding of the theory of non-linear partial differential equations, including existence and regularity results of free boundary value problems and applications to

**calculus of variations**.

The work of Prof. Ambrosio has a multitude of applications ranging from the descriptions of the chaotic motions observed in fluids, to characterizations of the equilibrium states of gases and to optimal mass transportation. Ambrosio’s work established

**unexpected connections**between his core area of research: partial differential equations and other research areas such as geometric measure theory, calculus of variations and

**infinite dimensional optimization**. During his career, Luigi Ambrosio built up at the Scuola Normale Superiore di Pisa a veritable school of mathematical analysis by mentoring a number of extremely talented young mathematicians who are themselves world leaders in mathematical research.