Geodesic
Regularity results for a class of obstacle problems
Applications of Mathematics, Tome 52 (2007) no. 2, pp. 137-170

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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. \[ L^{-1}|z|^p \le f(x,s,z) \le L(1+|z|^p). \]
DOI : 10.1007/s10492-007-0007-4
Classification : 35J85, 49J40, 49N60
Keywords: regularity results; local minimizers; integral functionals; obstacle problems; standard growth conditions 
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Eleuteri, Michela. Regularity results for a class of obstacle problems. Applications of Mathematics, Tome 52 (2007) no. 2, pp. 137-170. doi: 10.1007/s10492-007-0007-4

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