Joseph Feneuil

eWelcome

I am currently a MSI Fellow at the Australian National University. 

Previously, I did a Ph.D. in Grenoble (France) under the mentoring of Emmanuel Russ, then  held postdoctoral positions at the University of Minnesota (USA), Temple University (USA), Université Paris-Saclay (France), and the Università di Pisa (Italy).

Research Fields

My research interests lie in PDE, harmonic analysis and geometric measure theory. 

During my Ph.D.,  I worked on the Lp-boundedness of quadratic functionals or Riesz transforms on non-Euclidian spaces (graphs or Riemannian manifolds). One of my results established the Lp-boundedness of the Riesz transform for 1<p<2 of the Riesz transform on fractal-like graphs such as the one built from the Sierpinski gasket.

The main focus of my first postdoctoral positions was the study of boundary value problems on domains that are complement of a thin boundary. By means of degenerate elliptic operators in divergence form, Svitlana Mayboroda, Guy David, and I developed an ellipc theory on such sets, and then we started to study the relationship between the geometry of the boundary and the regularity of the solutions.