On the relaxation of nonconvex superficial integral functionals
Mandallena, Jean-Philippe
HAL, hal-01644831 / Harvested from HAL
Text on HAL
We present a new approach to the variational relaxation of functionals $F:D(\mathbb{R}^N;\mathbb{R}^m)\to[0,\infty[$ of the type:$$F(v):=\int_{\mathbb{R}^N}W(\nabla v(x))d\mu(x),$$where $W:\mathbb{R}^{mN}\to[0,\infty[$ is a continuous function with growth conditions of order $p\geq 1$ but not necessarily convex. We essentially study the case when $\mu$ is the $k$-dimensional Hausdorff measure restricted to a suitable piece of a $k$-dimensional smooth submanifold of $\mathbb{R}^N$.
Publié le : 2000-12-04
Classification:  [MATH]Mathematics [math] 
@article{hal-01644831,
     author = {Mandallena, Jean-Philippe},
     title = {On the relaxation of nonconvex superficial integral functionals},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01644831}
}

Mandallena, Jean-Philippe. On the relaxation of nonconvex superficial integral functionals. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-01644831/