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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. $L^{-1}| z| ^p \leq f(x,s,z) \leq L(1+| z| ^p).$

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