arXiv subjects
Publications and source records attributed to Maria Francesca Betta.
In the present paper we prove uniqueness results for solutions to a class of Neumann boundary value problems whose prototype is --div((1 + |$\nabla$u| 2) (p--2)/2 $\nabla$u) -- div(c(x)|u| p--2 u) = f in $Ω$, (1 + |$\nabla$u| 2) (p--2)/2 $\nabla$u + c(x)|u| p--2 u $\times$ n = 0 on $\partial$$Ω$,
In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is \begin{equation*} \begin{cases} -Δ_{p} u -\text{div} (c(x)|u|^{p-2}u)) =f & \text{in}\ Ω, \\ \left( |\nabla u|^{p-2}\nabla u+ c(x)|u|^{p-2}u \right)\cdot\underline n=0 & \text{on}\ \partial Ω\,, \end{cases} \end{equation*} when $f$ is just a summable function. Our approach allows also to deduce a stability result for renormalized solutions and an existence result for operator with a zero order term.