Elliptic problems in generalized Orlicz-Musielak spaces

• Autorzy: Piotr Gwiazda , Piotr Minakowski , Aneta Wróblewska-Kamińska
• Języki publikacji: EN

Abstrakty

EN

We consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.

Słowa kluczowe

EN

Orlicz Spaces; Nonlinear elliptic equations; log-Hölder continuity; Modular topology

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 35J60: Nonlinear elliptic equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 2019-2032

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Piotr Gwiazda

• Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

autor

Piotr Minakowski

• Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

autor

Aneta Wróblewska-Kamińska

• Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

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Identyfikatory

DOI

10.2478/s11533-012-0126-3