Regularity results for weak solutions of elliptic PDEs below the natural exponent

Abstract

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].

Several results corrected and revised. We would like to thank Doyoon Kim for pointing out an error in the previous version

Cited by in corpus (1)

• Two weight norm inequalities for fractional integral operators and commutators