Abstract
In this paper, we show that Orlicz–Sobolev spaces W^{1,varphi }(varOmega ) can be characterized with the ACL- and ACC-characterizations. ACL stands for absolutely continuous on lines and ACC for absolutely continuous on curves. Our results hold under the assumptions that C^1(varOmega ) functions are dense in W^{1,varphi }(varOmega ), and varphi (x,beta ) ge 1 for some beta > 0 and almost every x in varOmega . The results are new even in the special cases of Orlicz and double phase growth.
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