Large critical exponents for some second order uniformly elliptic operators.

Maria J. Esteban (1) , Patricio Felmer (2) , Alexander Quaas (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
3 Departamento de Matematica [Valparaiso]

In this paper we investigate the critical exponents of two families of Pucci's extremal operators. The notion of critical exponent that we have chosen for these fully nonlinear operators whihc are not variational is that of threshold betweeen existence and nonexistence of the solutions for semilinear equations with pure power nonlinearities. Interesting new exponents appear in this context.

Mots clés: Extremal operators; Pucci's operators; critical exponent

Domaines: Equations aux dérivées partielles [math.AP]

Maria J. Esteban, Patricio Felmer, Alexander Quaas. Large critical exponents for some second order uniformly elliptic operators.. Communications in Partial Differential Equations, 2007, 32 (4), pp.543-556. ⟨hal-00012841⟩