Boundary singularities of positive solutions of quasilinear Hamilton-Jacobi equations

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

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

We study the boundary behaviour of the solutions of (E) $\;-\Gd_p u+|\nabla u|^q=0$ in a domain $\Gw \sbs \BBR^N$, when $N\geq p> q>p-1$. We show the existence of a critical exponent $q_*

Mots clés: Schauder fixed point theorem; singularities; Leray-Lions operators; spherical p-harmonic equations; Key words p-Laplace operator

Domaines: Equations aux dérivées partielles [math.AP]

Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron. Boundary singularities of positive solutions of quasilinear Hamilton-Jacobi equations. 2015. ⟨hal-01095162v2⟩