Extremals for a Caffarelli-Khon-Nirenberg type inequality with cylindrical symmetry

Gianni Mancini, Università Roma 3

Abstract: We will discuss qualitative properties of extremals for a CKN type inequality possessing cylindrical symmetries. This inequality has been recently introduced by Badiale-Tarantello to handle some elliptic equations arising in some astrophysics problem. Cylindrical symmetry and suitable regulatity properties of the extremals can be used to completely identify them.