Renormalized solutions for a nonlinear parabolic equation with variable exponents and l(1)-data
By Mostafa Bendahmane, Petra Wittbold, A. Zimmermann. 2010
137 citations recorded by the source corpus.
Abstract We prove the well-posedness (existence and uniqueness) of a renormalized solution to nonlinear parabolic equations with variable exponents and L 1 -data. The functional setting involves Lebesgue–Sobolev spaces with variable exponents.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/18c6ff86f9ca7555affc5c116a15052fa9f2f6d0
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In Applied Mathematics
- Iwona Chlebicka
- Piotr Gwiazda
- A. Zimmermann
- Aneta Wróblewska
- Petra Wittbold
- Aneta Wróblewska-Kaminska
- Paolo Marcellini
In Mathematical Physics
- Iwona Chlebicka
- Piotr Gwiazda
- A. Zimmermann
- Aneta Wróblewska
- Petra Wittbold
- Aneta Wróblewska-Kaminska
- Paolo Marcellini
Citations in the corpus
- Renormalized solutions to nonlinear parabolic problems in generalized Musielak–Orlicz spaces (2015, background): “Thanks to the assumption (i), the spaces are reflexive and separable what significantly facilitates the considerations (see [7, 46]) since classical monotonicity methods are applicable.”
- A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, methodology): “Note that [24, 195] concern isotropic variable exponent spaces, while [22, 23, 141] the anisotropic”
- Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces (2012, background): “For results on existence of renormalized solutions of elliptic problems of type (E, f) with a(·, ·) satisfying a variable growth condition we refer to [20], [43] (for related results see also [9], [10], [42]).”