We review some recent results on log-weighted Moser type inequalities on the whole plane. The presence of a radial non decreasing weight prevents us applying the standard symmetrization approach. Nevertheless, we are able to prove that a Moser type inequality holds on a suitable log-mass weighted Sobolev space, without restricting ourselves to radial functions. We will discuss also some applications to nonlocal planar Choquard type equations with exponential critical growth. The results have been obtained partially in collaboration with Daniele Cassani (Università dell'Insubria).
Moser type log-mass weighted inequalities and exponential Choquard equations in the plane
C. Tarsi, Università degli Studi di Milano
2022 AWM Research Symposium
Analysis of Partial Differential Equations in Memory of David R. Adams