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PDF-thereverseinequalitycanbefalse.Weillustratethisphenomenonbythefollowin

PDF-thereverseinequalitycanbefalse.Weillustratethisphenomenonbythefollowin

Author : stefany-barnette | Published Date : 2015-11-08

fxsjsjlimr0supt2xrrx11Et2jsjThisfunctiondoesnotrepresentthefunctionalFonW1101IndeedifwechooseuxRx01Ecsdsthenu2W1101nC101andFuku0k112esssup01 fxux2No

f(x;s)=jsjlimr!0+supt2(xr;r+x)(1+1E(t))=2jsj:ThisfunctiondoesnotrepresentthefunctionalFonW1;1(0;1):Indeed ifwechooseu(x):=Rx01Ec(s)ds thenu2W1;1(0;1)nC1(0;1)andF(u)=ku0k1=12esssup(0;1) f(x;u(x))=2:No

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