Giovanni Leoni

Professor
Ph.D., University of Minnesota, Minneapolis

Office: Wean Hall 6128
Phone: (412) 268-2557
Fax: (412) 268-6380
E-mail: giovanni@andrew.cmu.edu

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.

Recent CNA Publications

• 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)

• 08-CNA-007, Gradient Theory for Plasticity via Homogenization of Discrete Dislocations , Adriana Garroni, Giovanni Leoni, Marcello Ponsiglione, (download paper)

All CNA Publications

Selected Publications

Books

1) Modern Methods in the Calculus of Variations: Lp Spaces, (in collaboration with I. Fonseca), Springer Monographs in Mathematics. Springer, New York, 2007.

2) Modern Methods in the Calculus of Variations: Sobolev Spaces, (in collaboration with I. Fonseca), in preparation, accepted for publication by Springer.

3) A First Course in Sobolev Spaces, Graduate Studies in Mathematics series, American Mathematical Society, Providence, RI, 2009.

Papers

1) On optimal regularity of free boundary problems and a conjecture of De Giorgi (in collaboration with H. Koch and M. Morini) Comm. Pure Appl. Math. 58 (2005), no. 8, 1051-1076;

2) Weak continuity and lower semicontinuity results for determinants (in collaboration with I. Fonseca and J. Malý Archive Rational Mech. Anal. 178 (2005), no. 3, 411-448;

3) Renormalized Energy and Forces on Dislocations (in collaboration with P. Cermelli) SIAM Journ. Math. Anal. 37 (2005), no. 4, 1131-1160;

4) Necessary and sufficient conditions for the chain rule in W^{1;1}_{loc}(R^N;R^d) and BV_{loc}(R^N;R^d) (in collaboration with M. Morini) J. Eur. Math. Soc. (JEMS) 9 (2007), no. 2, 219-252;

5) Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results, in collaboration with I. Fonseca, N. Fusco and M. Morini) Arch. Rational Mech. Anal. 186 (2007) 477-537;

6) A higher order model for image restoration: the one dimensional case, in collaboration with G. Dal Maso, I. Fonseca, and M. Morini, to appear in SIAM Journ. Math. Anal.

7) Gradient theory for plasticity via homogenization of discrete dislocations, in collaboration with A. Garroni and M. Ponsiglione, to appear in J. Eur. Math. Soc. (JEMS).