Alladi Ramakrishnan Hall

Nonlocal Boundary Hardy Inequality: The critical case

Prosenjit Roy

IIT Kanpur

Hardy's inequality plays an important role in the theory of partial differential equations. In this talk, we will be concerned with Hardy type inequalities, both classical and nonlocal versions. We will start with the classical Hardy's inequality and its developments. Then we will discuss non-local boundary Hardy type inequality and its generalised version, viz. non-local boundary Caffarelli-Kohn-Nirenberg inequality, in dimension one for the critical case (sp=1). The last part of the talk is based on a recent joint work with Adimurthi and Purbita Jana. If time permits, we will discuss the situation in higher dimensions.