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: L^p Spaces. Springer-Verlag, 2007.

Selected Publications in Journals

Fonseca, I. and S. Müller, “Relaxation of Quasiconvex Functionals in BV (Ω, R^p) for Integrands f(x, u, ∇u)", Arch. Rational Mech. Anal. 123 (1993), 1-49.

Fonseca, I. and J. Malý, “Relaxation of Multiple Integrals Below the Growth Exponent", Annales de L’Institut Henri Poincaré, Analyse Non Linéaire 14 (1997), 309–338.

Bouchitté, G., I. Fonseca and L. Mascarenhas, “A Global Method for Relaxation", Arch. Rat. Mech. Anal. 145 (1998), 51-98

Fonseca, I. and S. Müller, “A-Quasiconvexity: A Necessary and Sufficient Condition for Lower Semicontinuity Under PDE Constraints", SIAM J. Math. Anal. 30 (1999), 1355–1390.

Conti, S., I. Fonseca and G. Leoni, “A Gamma-Convergence Result for the Two-Gradient Theory of Phase Transitions”, CPAM 55 (2002), 857–936.

Bouchitté, G., I. Fonseca, G. Leoni and L. Mascarenhas,“A Global Method for Relaxation in W^{1,p} and in SBV^p”, Arch. Rat. Mech. Anal. 165 (2002), 187–242.

Fonseca, I., S. Müller and G. Leoni, “A-Quasiconvexity: Weak-Star Convergence and the Gap", Ann. Inst. Henri Poincaré -AN 21 (2004), 209–236.

Bouchitté, G., I. Fonseca and L. Mascarenhas, “The Cosserat Vector in Membrane Theory: A Variational Approach”, J. Convex Analysis 16 (2009), 351–365.

Fonseca, I., G. Leoni, F. Maggi and M. Morini, “Exact Reconstruction of Color Images Using a Total Variation Model”, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 1291–1331.

Fonseca, I., N. Fusco, G. Leoni and M. Morini, "Motion of Elastic Thin Films by Anisotropic Surface Diffusion with Curvature Regularization", Arch. Ration. Mech. and Anal. 205 (2012), 425–466.

Ferreira, R. and I. Fonseca, “Reiterated Homogenization in BV via Multiscale Convergence”, SIAM J. Math. Anal. 44 (2012), 2053–2098.

Dal Maso, G., I. Fonseca and G. Leoni, “Analytical Validation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces”, Arch. Ration. Mech. and Anal. 2014 (2014), 1037–1064.

Carozza, M., I. Fonseca and A. Passarelli di Napoli, “Regularity Results for an Optimal Design Problem with a Volume Constraint”, ESAIM:COCV 20 (2014), 460–487.

Choksi, R., Fonseca, I. and Zwicknagl, B., “A Few Remarks on Variational Models for Denoising”, Commun. Math. Sci., 12, (2014), 843-857.
Fonseca, I., N. Fusco, G. Leoni and M. Morini, “Motion of Three-Dimensional Elastic Films by Anisotropic Surface Diffusion with Curvature Regularization”, Anal. & PDE 8 (2015), 373–423.

Dal Maso, G., I. Fonseca and G. Leoni, “Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional”, Calc. Var. Partial Differential Equations 54 (2015), 1119–1145.

​Davoli, E. and I. Fonseca, “Homogenization of Integral Energies Under Periodically Oscillating Differential Constraints”, Calc. Var. Partial Differential Equations 55 (2016), 55–69. 

Fonseca, I., G. Leoni and M. Morini, “Equilibria and dislocations in epitaxial growth”. Nonlinear Anal. 154 (2017), 88-121. 

Videos

I. Fonseca. "Science of NHL Hockey: Vectors." NBC Learn video, 3:17. January 25, 2012. 

I. Fonseca. "Science of NHL Hockey: Mass, Volume & Density." NBC Learn video, 2:58. January 25, 2012. 

I. Fonseca. "Welcome to the SIAM Student Chapter in Delf UT." August 28, 2014.

I. Fonseca. "The Future of SIAM: Looking to the Mathematicians of Tomorrow ." 2017 SIAM Annual Meeting.