Homogénéisation du problème des courants de Foucault dans un transformateur
This paper is concerned with the following periodic Hamiltonian elliptic system Assuming the potential V is periodic and 0 lies in a gap of , is periodic in x and asymptotically quadratic in , existence and multiplicity of solutions are obtained via variational approach.
In this paper we prove that every weak and strong local minimizer of the functional where , f grows like , g grows like and 1<q<p<2, is on an open subset of Ω such that . Such functionals naturally arise from nonlinear elasticity problems. The key point in order to obtain the partial regularity result is to establish an energy estimate of Caccioppoli type, which is based on an appropriate choice of the test functions. The limit case is also treated for weak local minimizers. ...
We obtain in this paper a multiplicity result for strongly indefinite semilinear elliptic systems in bounded domains as well as in .