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operators
On the shape of the least-energy solutions to
some singularly perturbed mixed problems
In this paper we want to \emph{characterize} and
\emph{visualize} the shape of some solutions to a singularly
perturbed problem \eqref{eq:pe} with mixed Dirichlet and Neumann
boundary conditions. Such type of problem arises
in several situations as reaction-diffusion systems, nonlinear heat conduction and also as limit of reaction-diffusion systems coming from chemotaxis.
In particular we are interested in showing the location and
the shape of {\it least energy solutions} when the singular
perturbation parameter goes to zero, analyzing the geometrical
effect of the \emph{curved boundary} of the domain.