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[00218] Characterizations of diffusion matrices in homogenization of nondivergence-form elliptic equations

  • Session Time & Room : 3E (Aug.23, 17:40-19:20) @G501
  • Type : Contributed Talk
  • Abstract : We provide characterizations of diffusion matrices A for which the sequence of solutions $(u^{\varepsilon})_{\varepsilon > 0}$ to $-A(x/\varepsilon):D^2 u^{\varepsilon} = f$ in $\Omega$, $u^{\varepsilon} = g$ on $\partial\Omega$, converges to the solution of the homogenized problem with $L^{\infty}$-rate $\mathcal{O}(\varepsilon^2)$ for all sufficiently regular $f,g$. Whereas such diffusion matrices can be characterized via the third-order homogenized tensor, we provide more explicit characterizations and prove an open conjecture posed by Guo and Tran.
  • Classification : 35B27, 35B40, 35J25
  • Format : Talk at Waseda University
  • Author(s) :
    • Xiaoqin Guo (University of Cincinnati)
    • Timo Sprekeler (National University of Singapore)
    • Hung Vinh Tran (University of Wisconsin Madison)