Alvino, Angelo and Mercaldo, Anna:
Nonlinear Elliptic Equations with Lower Order Terms and Symmetrization Methods
Bollettino dell'Unione Matematica Italiana Serie 9 1 (2008), fasc. n.3, p. 645-661, (English)
pdf (432 Kb), djvu (143 Kb). | MR 2455337 | Zbl 1191.35125
Sunto
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.
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