Abstract
We establish the higher differentiability of solutions to a class of obstacle problems of the typeminâĄ{â«Î©f(x,Dv(x))dx:vâKÏ(Ω)}, where Ï is a fixed function called obstacle, KÏ(Ω)={vâWloc1,p(Ω,R):vâ„Ï a.e. in Ω} and the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher differentiability property of the weak solution v is related to the regularity of the assigned Ï, under a suitable Sobolev assumption on the partial map xâŠDΟf(x,Ο). The main novelty is that such assumption is independent of the dimension n and this, in the case pâ€nâ2, allows us to manage coefficients in a Sobolev class below the critical one W1,n.
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