ZhikovLaplace80Laplacep-Laplacep-Laplacepudiv(|u|p-3u)p>1p=2sLaplacep(x)-Laplacep(x)u=div(|u|p(x)-3u)p(x)RNp(x)-Laplacep(x)-Laplacep(x)-ZhikovLavrentievRNp1W^1p()W0^1p()Sobolevf:RNRCaratheodoryp1J(p)=inff(xu)dxuW0^1p()J(p)p1fffLavrentievfp-p1(x)RN:c1||^p-c0Q|f(x)|Qc2||^p+c0fLavrentievfp(x)-c1()^p-c0Q|f(x)|Qc2||^p+c0Zhikovp(x)fp(x)-ZhikovZhikovZhikov1.1p(x)Holderc1()^p-c0Q|f(x)|Qc2||^p+c0fZhikovp(x)-LaplaceSobolevLebesgue-SobolevW^kp|x|()SobolevLionsW^kp|x|()p(x)-LaplaceZhikov()
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