Improved Moser Trudinger inequality and Elliptic Eigen value problem

Moser Trudinger inequality comes in the limit case of Sobolev embedding.My talk will be on the derivation of an improved M-T inequality and then its application to prove the existence of principal eigenvalues for semilinear and quasilinear elliptic indefinite weight eigen value problem in the limiting dimension of sobolev imbeddings.Some more extension to higher order elliptic problem will also be discussed.