Recent Publications

• G. Leoni and R. Murray, Local minimizers and slow motion for the mass preserving Allen-Cahn equation in higher dimensions. Proc. Amer. Math. Soc. 147 (2019), no. 12, 5167–5182..
• G. Gravina and G. Leoni, Higher order gamma-limits for singularly perturbed Dirichlet-Neumann problems. SIAM J. Math. Anal. 51 (2019), no. 4, 3337–3372..
• G. Leoni and I. Tice, Traces for homogeneous Sobolev spaces in infinite strip-like domains. J. Funct. Anal. 277 (2019), no. 7, 2288–2380.
• I. Fonseca, G.Leoni, M.G. Mora, A Second Order Minimality Condition for a Free-Boundary Problem. Annali Scuola Normale Superiore di Pisa 19 (2019), no. 4, 1303-1358.
• G. Gravina and G. Leoni, On the behavior of the free boundary for a one-phase Bernoulli problem with mixed boundary conditions, Communications on Pure and Applied Analysis. 19 (2020), no. 10, 4853--4878.
• I. Fonseca and G.Leoni Surface evolution of elastically stressed films Eur. Math. Soc. Mag. (2021), no. 119, 31-39.
• G. Gravina and G. Leoni, On the existence of non-flat profiles for a Bernoulli free boundary problem. Advances in Calculus of Variations (ACV) 15 (2022), no. 1, 33-58
• G. Leoni and I. Tice , Traveling wave solutions to the free boundary incompressible Navier-Stokes equations, to appear in Comm. Pure Appl. Math..
• I. Fonseca, N. Fusco, G. Leoni, G. and M. Morini. Global and local energy minimizers for a nanowire growth model, to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire.  

For more publications, please go to:
http://www.math.cmu.edu/CNA/Publications/publications.php
http://cvgmt.sns.it/
https://arxiv.org/

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

Books

I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Lp Spaces, Springer Monographs in Mathematics. Springer, New York, 2007.

G. Leoni, A First Course in Sobolev Spaces, Graduate Studies in Mathematics. 105. Providence, RI: American Mathematical Society (AMS), 2009.

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

G. Leoni, A First Course in Fractional Sobolev Spaces,  Graduate Studies in Mathematics. 229. Providence, RI: American Mathematical Society (AMS), 2023.


I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Sobolev Spaces, in preparation, accepted for publication by Springer.