PDEs and Applications seminar: Elliptic Boundary Problems in Infinitesimally Flat Uniformly Rectifiable Domains

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

In this talk I will discuss recent results regarding the question of determining when singular integral operators of double layer type have small operator norms. The operator small norm estimates permit us to then establish solvability results for boundary value problems for a class of weakly elliptic second-order systems in sufficiently flat uniformly rectifiable domains, with boundary data from a library of function spaces. This includes Muckenhoupt weighted Lebesgue spaces, Lorentz spaces, Morrey spaces, and from Sobolev spaces naturally associated with these scales. This is joint work with J. J. Marin, J. M. Martell, D. Mitrea and M. Mitrea.