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Entropy and renormalized solutions to the general nonlinear elliptic equations in Musielak–Orlicz spaces |
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| Institution: | 1. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, PR China;2. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China;1. Institute of Mathematics, Polish Academy of Sciences, ul. ?niadeckich 8, 00-656 Warsaw, Poland;2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli, Via Cintia, 80126 Napoli, Italy;3. Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland |
| Abstract: | In this paper we mainly prove the existence and uniqueness of entropy solutions and the uniqueness of renormalized solutions to the general nonlinear elliptic equations in Musielak-Orlicz spaces. Moreover, we also obtain the equivalence of entropy solutions and renormalized solutions in the present conditions. |
| Keywords: | Entropy Renormalized Existence Uniqueness Elliptic Musielak–Orlicz spaces |
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