Giovanni Leoni

Giovanni Leoni is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University. His research interests include calculus of variations, partial differential equations, and geometric measure theory, with applications to continuum mechanics, materials science, and imaging. His recent work focuses on variational problems involving material defects, epitaxial growth, phase field models, and water waves. Leoni has authored several publications in leading mathematical journals and has contributed to the field through his research and teaching.

Giovanni Leoni is a Professor of Mathematics at Carnegie Mellon University, specializing in Calculus of Variations, Partial Differential Equations, and Materials Science. His research focuses on Sobolev spaces, fractional Sobolev spaces, and the calculus of variations, with applications to materials science and continuum mechanics. He has published extensively on topics such as Γ-convergence, relaxation in Sobolev spaces, and the mathematical modeling of dislocations and phase transitions in materials. His work also includes the study of regularity and existence results for free boundary problems and the analysis of renormalized energy in dislocation dynamics.