Abstracts

Exponential integrability in Logarithmically weighted Sobolev Spaces

Arka Mallick, Indian Institute of Science, Bangalore

In this talk, the embedding properties of weighted Sobolev spaces with logarithmic weights will be discussed. For a particular power of logarithm, the corresponding energy is related to the Leray energy. Notably, the Leray energy is weakly coercive due to the improvement of N-Hardy inequalities in dimension N. We explore this connection and present recent results concerning the optimal exponential integrability of functions within these spaces, yielding inequalities in the spirit of the Moser-Trudinger inequality. Finally, we will conclude by discussing the sharp versions of these inequalities when restricted to radial functions.