Seminario venerdì 6 luglio ore 14:30 del Prof. Nicolas Saintier (serie di Analisi Matematica)

We study the semilinear elliptic equation $$-\Delta u + g(u)\sigma = \mu$$ with Dirichlet boundary condition in a smooth bounded domain where $\sigma$ is a nonnegative Radon measure, $\mu$ a Radon measure and $g$ is an absorbing nonlinearity. We show that the problem is well posed if we assume that $\sigma$ belongs to some Morrey class. Un-der this condition we give a general existence result for any bounded measure provided $g$ satisfies a subcritical integral assumption. We study also the supercritical case when $g(r)= \abs r^{q-1}r$, with $q>1$ and $\mu$ satisfies an absolute continuity condition expressed in terms of some capacities involving $\sigma$. This is a joint work with Laurent Veron (Univ. Tours - France).