We study Moser–Trudinger type functionals in the presence of singular potentials. In particular we propose a proof of a singular Carleson–Chang type estimate by means of Onofri’s inequality for the unit disk in R2. Moreover we extend the analysis of Adimurthi (2004) and Csato and Roy (2015) considering Adimurthi–Druet type functionals on compact surfaces with conical singularities and discussing the existence of extremals for such functionals.
Extremal functions for singular Moser-Trudinger embeddings / Iula, Stefano; Mancini, Gabriele. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 156:(2017), pp. 215-248. [10.1016/j.na.2017.02.029]
Extremal functions for singular Moser-Trudinger embeddings
Mancini, Gabriele
2017
Abstract
We study Moser–Trudinger type functionals in the presence of singular potentials. In particular we propose a proof of a singular Carleson–Chang type estimate by means of Onofri’s inequality for the unit disk in R2. Moreover we extend the analysis of Adimurthi (2004) and Csato and Roy (2015) considering Adimurthi–Druet type functionals on compact surfaces with conical singularities and discussing the existence of extremals for such functionals.| File | Dimensione | Formato | |
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