- Porous Media: Interesting tools are needed to deal with degenerate diffusion and with hysteresis effects. Our results are on existence, approximation, and homogenization. High-light: Justification of a model for the fingering effect in porous media.
- Plasticity: The memory effect of plastic materials makes this poblem interesting. High-light: Stochastic homogenization of plasticity.
- Maxwell's equations: Homogenization in degenerate geometries and for large contrast materials. High-lights: Negative index meta-materials, geometric characterization of opaque materials, perfect transmission.
- Helmholtz equation: Resonance effects and radiation conditions. High-light: The spectrum of small Helmholtz resonators, effective acoustic properties of a medium with many small resonators, radiation conditions in periodic media.
Wave-equation: Dispersion on large time intervals. High-light: Effective dispersive equations for wave equations in arbitrary dimension and for wave equations on lattices.
Other research is on elasticity and Gamma-convergence, negative index materials (cloaking), transmission conditions, optimality problems, free boundary problems, fluid mechanics.