Irene Fonseca

Mellon College of Science Professor of Mathematics,
Director of Center for Nonlinear Analysis

Ph.D., University of Minnesota, Minneapolis

Office: Wean Hall 6123
Phone: (412) 268-3615
Fax: (412) 268-6380
E-mail: fonseca@andrew.cmu.edu

Research

My research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Recent work has been focused on the search for effective or relaxed energies, and on the study of existence, regularity, oscillatory and hysteretic behavior of solutions of (non convex) variational problems associated with materials instabilities, phase transitions, plasticity, nucleation and growth of phases, fracture and defects in solids. The applications which guide me in this program arise from the analysis of mathematical models for computer vision and imaging, as well as for novel man-made materials such as shape memory alloys, ferroelectric, magnetic and magnetostrictive materials, composites, liquid crystals, and thin films. The mathematical challenges lie in the description of the dynamics and evolution of microscopic structures and of phenomena that occur at vastly different temporal or spatial scales. They require recently developed mathematical tools and the introduction of new mathematical techniques.

Selected Publications

Books

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

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.

Selected Articles

Fonseca, I., Fusco, N., Leoni, G. and Morini, M., Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results. To appear in Arch. Ration. Mech. Anal.

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

Fonseca, I., Leoni, G. and Maly J., A-quasiconvexity: weak-star convergence and the gap. Ann. Inst. H. Poincare. Non Lineaire 21 (2004), no. 2, 209--236.

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.

Fonseca, I., Fusco, N. and Marcellini, P., On the total variation of the Jacobian. J. Funct. Anal. 207 (2004), no. 1, 1--32.

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.

Conti, S. Fonseca, I. and Leoni, G., A Gamma-convergence result for the two-gradient theory of phase transitions. Comm. Pure Appl. Math. 55 (2002), no. 7, 857--936.

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

Bouchitte., Fonseca, I. and Mascarenhas, L., A global method for relaxation. Arch. Rational Mech. Anal. 145 (1998), no. 1, 51--98.

Fonseca, I. Muller, S. and Pedregal, P., Analysis of concentration and oscillation effects generated by gradients. SIAM J. Math. Anal. 29 (1998), no. 3, 736--756.

Other Publications

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