On a Volume Constrained Variational Problem
with Lower Order Terms

Massimiliano Morini
and
Marc Oliver Rieger
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rieger@sns.it

ABSTRACT

We study a one-dimensional variational problem with two or more more level set constraints. The existence of global and local minimizers is surprisingly dependent on the regularity of the energy density. A c omplete characterization of local minimizers and the underlying energy landscape is provided. The $\Gamma$-limit when the phase exhaust the whole domain is com puted.

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