The paper deals with the problem of finding a curve, going through the interior of the domain $\Omega$, accross which the flux $\partial u/\partial n$, where $u$ is the solution of a mixed elliptic boundary value problem solved in $\Omega$, attains its maximum.

We consider singular perturbation variational problems depending on a small parameter $\epsilon$. The right hand side is such that the energy does not remain bounded as $\epsilon \to 0$. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with $\epsilon \>0$ are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating...

We consider singular perturbation variational problems depending on a small parameter ε. The right hand side is such that the energy does not remain bounded as ε → 0. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with ε > 0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after...