Department of         Mathematical Sciences
Events People Colloquia and Seminars Conferences Centers Positions Areas of Research About the Department
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 program is at the interface between pure and applied analysis, and is motivated by applications in the physical sciences and engineering. Her recent work is focused on variational techniques as they apply to contemporary problems in materials sciences and computer vision, and it includes the mathematical study of shape memory alloys, ferroelectric and magnetic materials, composites, liquid crystals, thin structures, phase transitions, epitaxy, and image segmentation, staircasing and recolorization in computer vision.

#### 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