Nils Dencker

The 2005 Clay Research Award was made to Nils Dencker for his complete resolution of a conjecture made by F. Trèves and L. Nirenberg in 1970.  This conjecture posits an essentially geometric necessary and sufficient condition, Psi, for a pseudo-differential operator of principal type to be locally solvable, i.e., for the equation Pu = ƒ to have local solutions given a finite number of conditions on ƒ.