| Issue |
ESAIM: COCV
Volume 9, February 2003
|
|
|---|---|---|
| Page(s) | 125 - 133 | |
| DOI | https://doi.org/10.1051/cocv:2003003 | |
| Published online | 15 September 2003 | |
Geometric constraints on the domain for a class of minimum problems
Dip. di Matematica, P.le Aldo Moro 2, 00185 Roma, Italy;
crasta@mat.uniroma1.it. malusa@mat.uniroma1.it.
Received:
27
March
2002
We consider minimization problems of the form
![${\rm min}_{u\in \varphi +W^{1,1}_0(\Omega)}\int_\Omega [f(Du(x))-u(x)]\, {\rm d}x$](/articles/cocv/abs/2003/01/cocv265/cocv265_tex_eq1.png)
where 
is a bounded convex open set, and the
Borel function ![$f\colon \mathbb{R}^N \to [0, +\infty]$](/articles/cocv/abs/2003/01/cocv265/cocv265_tex_eq3.png)
is assumed to be
neither convex nor coercive. Under suitable assumptions involving
the geometry of Ω and the zero level set of f, we prove
that the viscosity solution of a related Hamilton–Jacobi equation
provides a minimizer for the integral functional.
Mathematics Subject Classification: 49J10 / 49L25
Key words: Calculus of Variations / existence / non-convex problems / non-coercive problems / viscosity solutions.
© EDP Sciences, SMAI, 2003
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