Nirmalendu Chaudhuri

University of Wollongong (Australia)

On improved Hardy-Sobolev inequality and its application to partial differential equations with singular potential

It is well-known that the best constant in the classical Hardy-Sobolev inequality is never achieved in any domain, leaving room for an error estimate. In 1997 Brezis and Vasquez obtained an L2-improved inequality. But their estimate is far from being optimal. In this talk we will discuss the optimal Lp-improved Hardy-Sobolev inequality in all dimensions. We will also discuss various applications of the improved inequality to semi-linear partial differential equations involving the critical inverse square potentials.