Title: Regularity Estimates for PDE with Data in Non-Standard Spaces

Abstract: In this talk I present recent joint work with D. Cruz-Uribe. Given a weak super-solution $u\in W^{1,2}_0(\Omega)$ of the elliptic equation $$-\textrm{Div}\left(Q(x)\nabla u(x) \right) = f(x)$$ in a smooth domain $\Omega$ of $\mathbb{R}^n$ with $f$ in the Birnbaum-Orlicz space $L^A(\Omega)$ ($A(t) = t^{n/2}\log^\sigma(e+t)$ with $\sigma>n/2$) we show that $u$ satisfies$$\|u\|_{L^\infty(\Omega)} \leq C\|f\|_{L^A(\Omega)}$$with $C$ independent of both $u$ and $f$.  This talk will discuss many basic notions in the theory or Birnbaum-Orlicz spaces and is accessible to graduate students.