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Marcello Lucia, City University of New York

Abstract
The study of semilinear problems with exponential nonlinearity has already been addressed by Liouville in the context of the problem of prescribing Gaussian curvature on a two-dimensional domain.
For this class of semilinear problems, the structure of the solutions has been studied in detail and has revealed quantization phenomena for blowing-up sequences of solutions.
In higher dimension, there are some analogous problems involving now the n-Laplacian, and we will see how those quantization results can be generalized.
This is a joint work with Pierpaolo Esposito (Università di Roma 3)