Abstract
We study a nonlinear elliptic problem with an irregular obstacle in a bounded nonsmooth domain when the nonlinearity is merely asymptotically regular. We find an optimal regularity requirement on the associated nonlinearity and a minimal geometric condition on the boundary to ensure a global Calderón–Zygmund estimate for such an asymptotically regular obstacle problem. We assume that the associated nonlinearity has a small BMO and the boundary is sufficiently flat in the Reifenberg sense.
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