Regularity results for weak solutions of elliptic PDEs below the natural   exponent
  We prove regularity estimates for weak solutions to the Dirichlet problem for a divergence form elliptic operator. We give $L^p$ estimates for the second derivative for $p<2$. Our work generalizes results due to Miranda [28]. 
David Cruz-Uribe, Kabe Moen, and Scott Rodney
math.AP