| Abstract: |
| 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. Under 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
$g(r)=|r|^{q-1}r$, with $q>1$ and $\mu$ satisfies an absolute continuity condition expressed in terms of some capacities involving $\sigma$ |
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