We establish the natural Calderó n and Zygmund theory for solutions of elliptic and parabolic obstacle problems involving possibly degenerate operators in divergence form of p-Laplacian type, and proving that the (spatial) gradient of solutions is as integrable as that of the assigned obstacles. We also include an existence and regularity theorem where obstacles are not necessarily considered to be non-increasing in time.
The aim of this paper is to establish a Meyer's type higher integrability result for weak solutions of possibly degenerate parabolic systems of the typeThe vector-field a is assumed to fulfill a non-standard p(x, t)-growth condition. In particular it is shown that there exists ε > 0 depending only on the structural data such that there holds:loc , together with a local estimate for the p(·)(1 + ε)-energy.
In this paper we establish that the gradient of weak solutions to porous medium-type systems admits the self-improving property of higher integrability.
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