# sw NLPDE Z~i[

## sw NLPDE Z~i[Kyoto University NLPDE Seminar

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Room 251 at Science Building No.3, Kyoto University imapj
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### ̃Z~i[̗\Upcoming seminar

2016 N 7 29 @15:00  17:30 @y֐m_Z~i[Ƃ̋JÁz
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Room changed to 127 at Science Building No.3, Kyoto University
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Stefan Neukamm iTU Dresdenj
Ic v isww@wȁiFjj
Mikio Kurita (Kyoto University)
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y15:00-16:00@S. Neukammz
@Stochastic homogenization of nonconvex discrete energies with degenerate growth
y16:30-17:30@M. Kuritaz
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yS. Neukammz
The homogenization limit of discrete, nonconvex energy functionals defined on crystal lattices in dimensions $d \ge 2$ is well understood in the case of periodic or random pair interactions satisfying a uniform $p$-growth condition. In the talk I consider a degenerate situation, when the interactions obey a $p$-growth condition with a random growth weight $\lambda$. We show that if $\lambda$ satisfies the moment condition $\mathbb{E} [\lambda^{\alpha} + \lambda^{-\beta}] < \infty$ for suitable values of $\alpha$ and $\beta$, then the discrete energy $\Gamma$-converges to an integral functional with a non-degenerate energy density. In the scalar case (which covers the case of the random conductance model), it suffices to assume that $\alpha \ge 1$ and $\beta \ge \frac{1}{p-1}$ (which is just the condition that ensures the non-degeneracy of the homogenized energy density). In the general, vectorial case, we additionally require that $\alpha > 1$ and $\frac{1}{\alpha} + \frac{1}{\beta} \le \frac{p}{d}$. The talk is based on joint work with M. Schäffner (TU Dresden) and A. Schlömerkemper (U Würzburg).
yM. Kuritaz
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### ̃Z~i[̗\Schedules of future seminars

7 29
Stefan Neukamm iTU Dresdenj
Ic v isww@wȁiFjj
Mikio Kurita (Kyoto University)