Faculty Giovanni Leoni, Professor
Ph.D., University of Minnesota, Minneapolis
E-mail: giovanni@andrew.cmu.edu
Office: Wean Hall 6123
Phone: 412-268-2557

Research:

My current research interests lie in calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Selected Publications:

Books

Leoni, Giovanni, A first course in Sobolev spaces, Graduate Studies in Mathematics, 105. American Mathematical Society, Providence, RI, 2009.

Fonseca, Irene; Leoni, Giovanni, Modern methods in the calculus of variations: Lp spaces, Springer Monographs in Mathematics. Springer, New York, 2007.

Recent CNA Publications:

• 13-CNA-008, Calculus of Variations , Irene Fonseca, Giovanni Leoni, (download paper)
• 12-CNA-007, Analytical Validation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces , Irene Fonseca, Giovanni Leoni, Gianni Dal Maso, (download paper)
• 11-CNA-005, Material Voids in Elastic Solids With Anisotropic Surface Energies , Irene Fonseca, Nicola Fusco, Giovanni Leoni, Vincent Millot, (download paper)
• 11-CNA-003, Characterization of Sobolev and BV Space , Giovanni Leoni, Daniel Spector, (download paper)
• 11-CNA-002, Motion of Elastic Thin Films by Anisotropic Surface Diffusion with Curvature Regularization , Irene Fonseca, Nicola Fusco, Giovanni Leoni, Massimiliano Morini, (download paper)
• 10-CNA-007, Relaxation in $SBV_{p}(\Omega; S^{d-1})$ , Graça Carita, Irene Fonseca, Giovanni Leoni, (download paper)
• 10-CNA-001, Singular perturbation models in phase transitions for second order materials , Milena Chermisi, Irene Fonseca, Giovanni Leoni, Gianni Dal Maso, (download paper)
• 09-CNA-019, Exact Reconstruction of Damaged Color Images Using a Total Variation Model , Irene Fonseca, Giovanni Leoni, Francesco Maggi, Massimiliano Morini, (download paper)
• 09-CNA-011, Nonlocal Character of the Reduced Theory of Thin Films with Higher Order Perturbations , Irene Fonseca, Giovanni Leoni, Gianni Dal Maso, (download paper)
• 08-CNA-010, A Higher Order Model for Image Restoration: The One Dimensional Case , Irene Fonseca, Giovanni Leoni, Gianni Dal Maso, Massimiliano Morini, (download paper)