MINIMIZERS AND GAMMA-CONVERGENCE OF ENERGY FUNCTIONALS DERIVED FROM $p$-LAPLACIAN EQUATION
MINIMIZERS AND GAMMA-CONVERGENCE OF ENERGY FUNCTIONALS DERIVED FROM $p$-LAPLACIAN EQUATION
This paper presents the existence of minimizers and $\Gamma$-convergence for the energey functionals \begin{eqnarray*} E_\epsilon(u) = \int_\Omega \left\{ W(u(x))+\epsilon{|\nabla u(x)|^p}\right\} dx, \mbox{ for all }\epsilon>0,\quad p>1 \end{eqnarray*} with Neumann boundary condition and the constraint \begin{eqnarray*} \int_\Omega u(x) dx = m|\Omega|, \mbox{ where }0 \lt m \lt 1. \end{eqnarray*} The energy …