PDE och tillämpningar: Higher-order convergence rates in periodic homogenisation of nonlinear PDEs

  • Datum: –11.15
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Sunghan Kim
  • Arrangör: Matematiska institutionen
  • Kontaktperson: Kaj Nyström
  • Seminarium

Abstract:  In this talk, I am going to talk about higher-order convergence rates in periodic homogenisation problems. When a highly oscillating PDE is homogenised, the solution to the oscillating PDE can be approximated by the homogenised solution and the associated correctors. The first-order corrector is well understood, and has been the centre of the analysis in homogenisation theory for many years. The second or higher-order correctors have been studied relatively less, but they contain some interesting information on how the rapidly oscillating structure on the background is mixed with the nonlinear structure of the given PDE. Here I am going to present some recent results on this issue, in the framework of fully nonlinear elliptic/parabolic PDEs, based on a series of joint work with K.-A. Lee.