Gradient estimates for obstacle problems with general nonlinearity under mean oscillation condition

초록

We establish local Calder & oacute;n-Zygmund type estimates for obstacle problems with general nonlinearities under a quasi-isotropic $(p,q)$-growth condition. The nonlinearity is assumed to satisfy a BMO-type mean oscillation condition in the spatial variable, which may allow for possible discontinuities. In this paper, we not only extend our previous results from equations in [46] to variational inequalities, but also refine the assumptions on oscillation further. Our results unify existing Calder & oacute;n-Zygmund estimates in special cases, such as the standard growth case with a BMO coefficient, the variable exponent case, the double phase case, and their borderline cases.

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