In collaboration with Ros Oton and Serra we develop the regularity theory for obstacle problem solutions to the obstacle problem. This involves the development of several new techniques.

Luis Caffarelli currently holds the Sid Richardson Chair at the University of Texas at Austin. In 1991 he was elected to the US National Academy of Sciences. He has received numerous honors and awards including the Stampacchia Medal from the Italian Mathematical Union, the Bocher Memorial Prize from the American Mathematical Society and the Rolf Schock Prize from the Swedish Academy of Sciences. He also received the Leroy P. Steele Prize for Lifetime Achievement in Mathematics from the American Mathematical Society. In 2012 he received the Wolf Prize.