Uniqueness results for nonlinear elliptic problems with two lower order terms
The authors consider Dirichlet problems for nonlinear elliptic equations of the form \[ \begin{cases} -\text{div\,}\big({\mathbf a}(x,\nabla u) +\pmb\Phi(x,u)\big)+H(x,\nabla u) =f & \text{in}\;\Omega\\ u=0 & \text{on}\;\partial\Omega, \end{cases} \] where \(\Omega\subset \mathbb R^N\) is a bounded open subset, \(N>2\) and \(f\in L^1(\Omega).\) Under suitable structural conditions on \({\mathbf a},\) \(\pmb\Phi\) and \(H\) (some of these natural) uniqueness results are derived via rearrangement techniques for the solutions obtained as limit of approximations.
scientific article; zbMATH DE number 6145427