Umberto Guarnotta (Catania) – Seminario di Analisi

Martedì, 2 Dicembr – Sala Professori I livello ore 15:00 – 16:00

A p-LAPLACIAN PROBLEM IN RN WITH SINGULAR, CONVECTIVE, CRITICAL REACTION

This talk is devoted to discuss existence, regularity, and decay properties of solutions to a p-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction. The approach used combines variational methods, truncation techniques, and concentration compactness arguments, together with set-valued analysis and fixed point theory. De Giorgi’s technique, a priori gradient estimates, and nonlinear regularity theory are employed to obtain local Hölder regularity of gradients of solutions, as well as their pointwise decay at infinity. The result is new even in the non-singular case, also for the Laplacian.