A Harnack type inequality for singular Liouville type equations

We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actually more delicate and results in a nontrivial variation of the regular case. Part of the arguments of Chen-Lin can be adapted to the singular case by means of an isoperimetric inequality for surfaces with conical singularities. The rest of the proof actually requires a different approach, due to the loss of translation invariance of the problem.
Nota: Questo seminario rientra tra le attività del progetto MUR "Dipartimenti d'eccellenza" MatMod@TOV (2023-27)