Global and local estimates for nonlinear noncoercive elliptic equations with measure data

Abstract

We study nonlinear noncoercive elliptic problems with measure data, proving first that the global estimates already known when the problem is coercive are still true for noncoercive problems. We then prove new estimates, on sets far from the support of the singular part of the right-hand side, in the energy space associated to the operator, which entails additional regularity results on the solutions.