# Giovanni Leoni

## Professor

**Address:**

6123 Wean Hall

Department of Mathematical Sciences

Carnegie Mellon University

5000 Forbes Avenue

Pittsburgh, PA 15213

**P:** 412-268-2557

# Education

Master in Mathematical Sciences, University of Minnesota

Ph.D. in Mathematics, University of Minnesota

# Awards

- Richard Moore Award, 2019
- Giuseppe Bartolozzi Award

# 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, in materials science, and in imaging. Recent areas of focus have been: variational problems involving material defects, such as dislocations; the epitaxial growth of a thin film over a crystalline substrate; phase field models for anisotropic crystalline energies; phase transitions problems; water waves.

# Select Publications

Fonseca, I., Leoni, G., and Mora, M.G. A Second order minimality condition for a free-boundary problem. *To appear in Annali Scuola Norm. Sup. Pisa Scien. Fis. Mat*.

Leoni, G. and Murray, R. Local minimizers and slow motion for the mass preserving Allen--Cahn equation in higher dimensions. *To appear in Proceedings American Mathematical Society*.

Fonseca, I., Fusco, N., Leoni, G., and Morini, M. (2018). A model for dislocations in epitaxially strained elastic films.* J. Math. Pures Appl*. (9) 111, 126-160.

Dal Maso, G., Fonseca, I. and Leoni, G. (2018). Asymptotic analysis of second order nonlocal Cahn-Hilliard-type functionals. *Trans. Amer. Math. Soc*., 370(4), 2785-2823.

Leoni, G. (2017). A First Course in Sobolev Spaces, Second edition. Graduate Studies in Mathematics, 181. *American Mathematical Society, Providence, RI*.

Leoni, G. and Murray, R. (2016). Second-order Gamma-limit for the Cahn--Hilliard functional. *Arch. Rational Mech. Anal.* 219, 1383-1451.

Blass, T., Fonseca, I., Leoni, G., and Morandotti, M. (2015). Dynamics for systems of screw dislocations. *SIAM J. Appl. Math.* 75, (2), 393-419.

Fonseca, I. and Leoni, G. (2015). Calculus of variations, The Princeton Companion to Applied Mathematics. *Princeton University Press*.

Fonseca, I., Fusco, N., Leoni, G., and Morini, M. (2015). Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization. *Anal. PDE*, 8 (2), 373-423.

Leoni, G. (2014). A remark on the compactness for the Cahn-Hilliard functional. *ESAIM: Control, Optimization and Calculus of Variations*, 20, 517-523.

Fonseca, I. and Leoni, G. (2007). Modern Methods in the Calculus of Variations: L^{p} Spaces, Springer Monographs in Mathematics. *Springer, New York.*

Koch, H., Leoni, G. and Morini, M. (2005). On optimal regularity of free boundary problems and a conjecture of De Giorgi. *Comm. Pure Appl. Math*. 58, 1051-1076.