Existence of renormalized solutions to nonlinear elliptic equations with two lower order terms and measure data
Olivier Guibé, Anna Mercaldo · Transactions of the American Mathematical Society · 2007
In this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is (P) { − △ p u − div ( c ( x ) | u | γ ) + b ( x ) | ∇ u | λ = μ a m p ; in Ω , u = 0 a m p ; in ∂ Ω , \begin{equation}\tag {P} \begin {cases} - \bigtriangleup _p u -\operatorname {div}(c(x)|u|^{\gamma })+b(x)| abla u|^{\lambda } =\mu & \text {in $\Omega $},\\ u=0 & \text {in $\partial \Omega $}, \end{cases} \end{equation} where Ω \Omega is a bounded open subset of R