Scientific publications
2012PreprintEnglishOpen access
Homogenization of a nonlinear elliptic problem with large nonlinear\n potential (opens in a new tab)
Authors
University of Yaoundé I
Other authors
Nils Svanstedt
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Scientific publications
Nils Svanstedt
arXiv (Cornell University)
Homogenization is studied for a nonlinear elliptic boundary-value problem\nwith a large nonlinear potential. More specifically we are interested in the\nasymptotic behavior of a sequence of p-Laplacians of the form $$\n-\\text{div}(a(\\frac{x}{\\varepsilon})|Du_\\varepsilon|^{p-2}Du_\\varepsilon)\n+\\frac{1}{\\varepsilon}V(\\frac{x}{\\varepsilon})|u_\\varepsilon|^{p-2}u_\\varepsilon=f.\n$$ It is shown that, under a centring condition on the potential $V$, there\nexists a two-scale homogenized system with solution $(u, u_1)$ such that the\nsequence $u_\\varepsilon$ of solutions converges weakly to $u$ in $W^{1,p}$ and\nthe gradients $D_x u_\\varepsilon$ two-scale converges weakly to $D_x u+ D_y\nu_1$ in $L^p$, respectively. We characterize the limit system explicitly by\nmeans of two-scale convergence and a new convergence result.\n