Faculty Irene Fonseca, Mellon College of Science Professor of Mathematics,
   Director of Center for Nonlinear Analysis
Ph.D., University of Minnesota, Minneapolis
E-mail: fonseca AT andrew DOT cmu DOT edu
Office: Wean Hall 6212
Phone: 412-268-3615

Research:

Irene Fonseca's research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Her research program is centered on the mathematical study of phenomena that occur at vastly different temporal or spatial scales, issuing from materials science and computer vision. These include the study of novel man-made materials such as shape memory alloys, magnetic materials, composites, liquid crystals, thin structures, phase transitions, and imaging.

Science of NHL Hockey: (Write-up in the New York Times about the hockey series.)

Science of NHL Hockey: Mass, Volume & Density

Science of NHL Hockey: Vectors

Selected Publications:

Books

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

I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Sobolev Spaces, to appear in Springer.

I. Fonseca and W. Gangbo, Degree Theory in Analysis and Applications. Oxford University Press, 1995.

Selected Articles

G. Dal Maso, I. Fonseca, G. Leoni anbd M. Morini, A higher order model for image restoration: the one dimensional case. To appear in SIAM Journ. Math. Anal.

Fonseca, I., Fusco, N., Leoni, G., Morini, M., Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results, Arch. Ration. Mech. Anal. 186} (2007), no. 3, 477--537.

Fonseca, I., Morini, M. and Slastikov, V., Surfactants in foam stability: a phase-field model. Arch. Ration. Mech. Anal. 183 (2007), no. 3, 411--456.

Fonseca, I., Leoni, G. and Malý, J., Weak continuity and lower semicontinuity results for determinants. Arch. Ration. Mech. Anal. 178 (2005), no. 3, 411--448.

Dal Maso, G., Fonseca, I., Leoni, G. and Morini, M., Higher-order quasiconvexity reduces to quasiconvexity. Arch. Ration. Mech. Anal. 171 (2004), no. 1, 55--81.

Bouchitte., Fonseca, I, Leoni, G. and Mascarenhas, L., A global method for relaxation in $W^{(1,p)}$ and in $SBV_p$. Arch. Ration. Mech. Anal. 165 (2002), no. 3, 187--242.

Dacorogna, B. and Fonseca, I. A-B quasiconvexity and implicit partial differential equations. Calc. Var. Partial Differential Equations 14 (2002), no. 2, 115--149.

Fonseca, I. and Müller, S. A-quasiconvexity, lower semicontinuity, and Young measures. SIAM J. Math. Anal. 30 (1999), no. 6, 1355--1390

Recent CNA Publications:

• 13-CNA-010, Regularity Results for an Optimal Design Problem with a Volume Constraint , Menita Carozza , Irene Fonseca, Antonia Passarelli, (download paper)
• 13-CNA-008, Calculus of Variations , Irene Fonseca, Giovanni Leoni, (download paper)
• 12-CNA-008, A Note on Variational Models for Denoising , Rustum Choksi, Irene Fonseca, Barbara Zwicknagl, (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-006, Reiterated Homogenization in BV via Multiscale Convergence , Rita Ferreira, Irene Fonseca, (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-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-018, Characterization of the Multiscale Limit Associated with Bounded Sequences in BV , Rita Ferreira, Irene Fonseca, (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)