Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods

Alvino, Angelo ; Mercaldo, Anna

Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 3, pp. 645-661

Résumé

We consider the homogeneous Dirichlet problem for nonlinear elliptic equations as \begin{equation*}-\operatorname{div} a(x, \nabla u) = b(x, \nabla u) + \mu \end{equation*} where $\mu$ is a measure with bounded total variation. We fix structural conditions on functions $a$, $b$ which ensure existence of solutions. Moreover, if $\mu$ is an $L^1$ function, we prove a uniqueness result under more restrictive hypotheses on the operator.