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

Jerome Droniou (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: Non-linear elliptic equations; measures; non-coercivity; local estimates

Domaines: Equations aux dérivées partielles [math.AP]

Jerome Droniou. Global and local estimates for nonlinear noncoercive elliptic equations with measure data. Communications in Partial Differential Equations, 2003, 28, pp.no 1-2, 129-153. ⟨10.1081/PDE-120019377⟩. ⟨hal-00003935⟩