... for his highly original and profound contributions to applied mathematics, calculus of variations and nonlinear partial differential equations, the mechanics of continua, and mathematical material sciences.

... for his work in many areas of applied mathematics ranging from fluid dynamics to condensed matter physics, including incompressible flows, turbulence, statistical physics, superconductivity, liquid crystals and polymers, epitaxial growth, and micromagnetics.

... for his fundamental contributions in areas ranging from micromagnetics, to coarsening rates during phase separation, to mass transportation problems. His work has given these areas a sense of clarity and definitiveness that has gone far beyond the reach of existing heuristic arguments.

... in recognition of his outstanding contributions to numerical solution of wave propagation problems and compressive sensing, as well as anisotropic extensions of wavelets.

... for the use of highly sophisticated mathematical techniques to produce fundamental breakthroughs that are applied to computer simulations in industry.

... for his breakthrough contributions that skillfully combine modelling of real world problems and rigorous mathematical analysis with the development of efficient and accurate numerical schemes and high performance computing.

... for her fundamental contributions to the regularity theory and the analysis of singularities in elliptic PDEs, geometric variational problems, transport equations, and incompressible fluid dynamics.