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Article

Keywords:
regularity results; local minimizers; integral functionals; obstacle problems; standard growth conditions
Summary:
We prove some optimal regularity results for minimizers of the integral functional $\int f(x,u,Du)\mathrm{d}x$ belonging to the class $ K:=\lbrace u \in W^{1,p}(\Omega )\: u\ge \psi \rbrace $, where $\psi $ is a fixed function, under standard growth conditions of $p$-type, i.e. \[ L^{-1}|z|^p \le f(x,s,z) \le L(1+|z|^p). \]
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