Nonlinear diffusion in transparent media: the resolvent equation

Lorenzo Giacomelli, Salvador Moll, Francesco Petitta

We consider the partial differential equation $$u-f=\mathrm{div}\left(u^m\frac{\nabla u}{|\nabla u|}\right)$$ with $f$ nonnegative and bounded and $m\in \mathbb{R}$. We prove existen…