Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry

Ovidiu Costin (1) , Louis Dupaigne (2)

1 Mathematics Department, The Ohio State University
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

We calculate the full asymptotic expansion of boundary blow-up so- lutions, for any nonlinearity f . Our approach enables us to state sharp qualitative results regarding uniqueness and ra- dial symmetry of solutions, as well as a characterization of nonlinearities for which the blow-up rate is universal. At last, we study in more detail the standard nonlinearities f (u) = u^p , p > 1

Domaines: Equations aux dérivées partielles [math.AP]

Ovidiu Costin, Louis Dupaigne. Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry. 2009. ⟨hal-00356579v3⟩