| Abstract: |
| In this talk, we consider double phase problems in divergence form on bounded domains. A double phase problem is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We first prove a global Calderon-Zygmund type estimate for a double phase problem with $(p,q)$-growth in the case that the boundary of the domain is of class $C^{1,\beta}$ for some $\beta>0$. And then we present a similar result for the borderline case of the above problem in the case that the associated nonlinearity has a small BMO and the boundary of the domain is sufficiently flat in the Reifenberg sense. |
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