Non uniqueness for the Dirichlet problem for fully nonlinear elliptic operators - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2006

Non uniqueness for the Dirichlet problem for fully nonlinear elliptic operators

Boyan Sirakov
  • Fonction : Auteur
  • PersonId : 829996

Résumé

We study uniformly elliptic fully nonlinear equations of the type $F(D^2u, Du, u, x)=f(x)$ in $\Omega$, where $F$ is a convex positively 1-homogeneous operator and $\Omega$ is a regular bounded domain in $\rn$. We prove non-existence and multiplicity results for the Dirichlet problem, when the two principal eigenvalues of $F$ are of different sign. Our results extend to more general cases, for instance, when $F$ is not convex, and explain in a new light the classical Ambrosetti-Prodi phenomenon in elliptic theory.
Fichier principal
Vignette du fichier
NonUniq.pdf (152.76 Ko) Télécharger le fichier

Dates et versions

hal-00079186 , version 1 (09-06-2006)
hal-00079186 , version 2 (09-01-2009)
hal-00079186 , version 3 (30-01-2015)

Identifiants

  • HAL Id : hal-00079186 , version 1

Citer

Boyan Sirakov. Non uniqueness for the Dirichlet problem for fully nonlinear elliptic operators. 2006. ⟨hal-00079186v1⟩
95 Consultations
406 Téléchargements

Partager

Gmail Facebook X LinkedIn More