The impact of a lower order term in a Dirichlet problem with a singular nonlinearity
Lucio Boccardo, Gisella Croce · Portugaliae Mathematica · 2020
In this paper we study the existence and regularity of solutions to the following Dirichlet problem \begin{cases} -\operatorname{div}(a(x)| abla u|^{p-2} abla u) + u|u|^{r-1} = \frac{f(x)}{u^{\theta}} & \text{in }\Omega, \\ u > 0 & \text{in }\Omega, \\ u = 0 & \text{on }\partial\Omega \end{cases} proving that the lower order term u|u|^{r-1} has some regularizing effects on the solutions.