Calculus of Variations and Geometric Measure Theory

G. P. Leonardi - P. Tilli

On a constrained variational problem in the vector-valued case

created by leonardi on 17 Dec 2006


Published Paper

Inserted: 17 dec 2006

Journal: J. Math. Pures Appl.
Volume: 85
Pages: 251-268
Year: 2006


We prove some existence and regularity results for minimizers of a class of integral functionals, defined on vector-valued Sobolev functions $u$ for which the volumes of certain level-sets $\{u=l_i\}$ are prescribed, with $i=1,\dots,m$. More specifically, in the case of the energy density $W(x,u,D u) =
D u
^2 + \beta F(u)$, we prove that minimizers exist and are locally Lipschitz, if the function $F$ and $\{l_1,\dots,l_m\}$ verify suitable hypotheses.