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Regularity results for a class of obstacle problems. (English) Zbl 1164.49009
Summary: We prove some optimal regularity results for minimizers of the integral functional \(\int f(x,u,Du)\,\text dx\) belonging to the class \(K:=\{u \in W^{1,p}(\Omega )\: u\geq \psi \}\), where \(\psi \)  is a fixed function, under standard growth conditions of \(p\)-type, i.e. \[ L^{-1}| z| ^p \leq f(x,s,z) \leq L(1+| z| ^p). \]

49N60 Regularity of solutions in optimal control
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49J40 Variational inequalities
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