The PDEs and Applications seminar: Strong maximum principle and boundary estimates for nonlinear nonhomogeneous elliptic PDEs

  • Date: –11:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Niklas Lundström
  • Organiser: Matematiska institutionen
  • Contact person: Kaj Nyström
  • Seminarium

Abstract:  We consider viscosity solutions of fully nonlinear nonhomogeneous elliptic PDEs on the form F(x,u,Du,D^2u) = 0.

We show how to construct some classical solutions which we use to give a proof of the strong maximum principle for viscosity subsolutions. In case of smooth boundaries, we also prove the Hopf lemma and that positive viscosity solutions vanishing on a portion of the boundary are comparable with the distance function near the boundary.