A priori estimates for elliptic equations with reaction terms involving the function and its gradient

Marie-Françoise Bidaut-Véron (1) , Marta Garcia-Huidobro (2) , Laurent Veron (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 Departamento de Matemáticas [Santiago de Chile]

We study local and global properties of solutions of −∆u = u p + M ||u| q in a domain Ω of R N , in the range min{p, q} > 1 and M ∈ R. We prove a priori estimates and existence or non-existence of ground states.

Mots clés: elliptic equations; Bernstein methods; ground states

Domaines: Equations aux dérivées partielles [math.AP]

Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Veron. A priori estimates for elliptic equations with reaction terms involving the function and its gradient. Mathematics Subject Classification. 35J62, 2018, 35. ⟨hal-01906697v1⟩