I work near the boundary between harmonic analysis and partial differential equations. My research tries to find optimal (or at least better) conditions for several problems in partial differential equations. Over the years, I have considered questions about regularity of solutions to parabolic equations in Lipschitz domains, minimal a priori regularity conditions to allow uniqueness in inverse boundary value problems, regularity questions related to the inverse scattering method for a non-linear evolution equation in two dimensions. The last area of research led to considering weighted estimates for Brascamp-Lieb forms.