Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces

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• 作者：Piotr Gwiazda^a ; ^{pgwiazda@mimuw.edu.pl} ; Petra Wittbold^b ; ^{petra.wittbold@uni-due.de} ; Aneta Wró ; blewska^a ; ^{a.wroblewska@mimuw.edu.pl} ; Aleksandra Zimmermann^b ; ^{zimmermann.aleksandra@uni-due.de}
• 关键词：35J60 ; 35D05
• 刊名：Journal of Differential Equations
• 出版年：2012
• 期刊代码：74_00220396
• 类别：mt
• 出版时间：15 July, 2012
• 卷：253
• 期：2
• 页码：635-666
• 文件大小：321 K

摘要

We study a general class of nonlinear elliptic problems associated with the differential inclusion , where . The vector field is monotone in the second variable and satisfies a non-standard growth condition described by an x-dependent convex function that generalizes both and classical Orlicz settings. Using truncation techniques and a generalized Minty method in the functional setting of non-reflexive spaces we prove existence of renormalized solutions for general -data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established. Sufficient conditions are specified which guarantee that the renormalized solution is already a weak solution to the problem.