Alladi Ramakrishnan Hall

Some functional Inequalities on Sobolev Spaces

Prosenjit Roy

IIT Kanpur

Starting from the definition of weak derivatives, we will see some aspects of Sobolev spaces in this talk. Then the main aim of this talk is to present some functional inequalities like Poincar\'e, Sobolev, Moser-Trudinger inequalities on these spaces and see how they are connected to solutions of some PDEs. If time permits, some results concerning singular Moser Trudinger (due Adimurthi Sandeep) inequality will be presented. The talk will be kept at an elementary level.