Giovanni Leoni

Giovanni Leoni is a Full Professor at Carnegie Mellon University, specializing in mathematical analysis with a focus on partial differential equations (PDEs), calculus of variations, and their applications to materials science and mathematical finance. His research explores topics such as Gamma-convergence, phase transitions, free boundary problems, and nonlinear elasticity. He has contributed to foundational works on Sobolev spaces and their applications in PDE theory.

Leoni's notable publications include studies on the Cahn-Hilliard functional, elastic thin films, and epitaxial growth models. He has collaborated extensively with leading researchers such as Irene Fonseca and Gianni Dal Maso. His textbook A First Course in Sobolev Spaces serves as a key resource in the field.

Recent research highlights include second-order Γ-limits for the Cahn-Hilliard functional with Dirichlet boundary conditions, analysis of elastic thin film dewetting, and equilibrium models in financial mathematics. His work bridges theoretical analysis with applied problems in materials science and economics.