On the Abel Prize to L. Nirenberg and John Nash

On the Abel Prize to L. Nirenberg and John Nash

Many in the Math-community feel let down that there is no Nobel for Mathematicians. But in fact there are several prizes to encourage budding mathematicians. One such is the Abel Prize which people say is an answer to the question of ‘no Nobel for math’. The prize money is also incredibly attractive!
On May 19 2015, Louis Nirenberg and John Nash received the famed Abel prize which includes a citation, gold medal and 6 Million NOK (Norwegian Currency Norway Kroner) which approximately amount to Rs 5,00,00,000. The citation says “For striking and seminal contributions to the theory of non-linear PDE’s and it’s applications to geometric analysis”
Solutions to certain differential equations arising in nature were hard to find and then one
George de Rham (a Swiss mathematician) gave the so called weak solution. The works of Louis Nirenberg and John Nash show that these solutions can be rendered ‘regular’. John Nash(of the Beautiful Mind fame) besides the work on game theory also worked on Holder estimates for the solutions of linear elliptic equations in general dimension without any regularity assumptions. This led to the solution of Hilbert’s 19^th problem. Similarly Nirenberg made beautiful application of the so called maximum principles which refer to certain analytic results on the attainment of maximum bounds on some small domains in the context of non-linear elliptic partial differential equations.
Applications of these works include the solution of the prescribed curvature problem in geometry, the Navier-Stokes problems, stability of the GNS inequalities(named after Gagliardo-Nirenberg-Sobolev) and problems involving GR(General Relativity) in cosmology.
Other recipients include S. R. S. Varadhan, Yakov Sinai, and Peter Lax. The latest recipient of the Abel Prize is a leading women mathematician- Karen Uhlenbeck of the University of Texas at Austin.