Existence and homogenization of nonlinear elliptic systems in nonreflexive spaces

We consider a strongly nonlinear elliptic problem with the homogeneous Dirichlet boundary condition. The growth and the coercivity of the elliptic operator is assumed to be indicated by an inhomogeneous anisotropic N-function. First, an existence result is shown under the assumption that the N-funct...

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Published inNonlinear analysis Vol. 194; p. 111487
Main Authors Bulíček, Miroslav, Gwiazda, Piotr, Kalousek, Martin, Świerczewska-Gwiazda, Agnieszka
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.05.2020
Elsevier BV
Subjects
Boundary conditions
Coercivity
Dirichlet problem
Existence of solution
Fast growth
Homogenization
Musielak–Orlicz spaces
Nonlinear elliptic problem
Nonlinear systems
35B27
Nonlinear elliptic problem
Fast growth
Existence of solution
Homogenization
76M50
Musielak–Orlicz spaces
35J47
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Summary:We consider a strongly nonlinear elliptic problem with the homogeneous Dirichlet boundary condition. The growth and the coercivity of the elliptic operator is assumed to be indicated by an inhomogeneous anisotropic N-function. First, an existence result is shown under the assumption that the N-function or its convex conjugate satisfies Δ2-condition. The second result concerns the homogenization process for families of strongly nonlinear elliptic problems with the homogeneous Dirichlet boundary condition under above stated conditions on the elliptic operator, which is additionally assumed to be periodic in the spatial variable.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.03.010