Abstract
In this work, we study the existence of at least one renormalized solution for a p(.)-Laplacian equation associated with a maximal monotone operator and a nonlinear Neumann boundary condition. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.
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Communicated by Julio Rossi.
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Benboubker, M.B., Nassouri, E., Ouaro, S. et al. Renormalized solutions for p(x)-Laplacian equation with Neumann nonhomogeneous boundary condition. Adv. Oper. Theory 5, 1480–1497 (2020). https://doi.org/10.1007/s43036-020-00055-9
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DOI: https://doi.org/10.1007/s43036-020-00055-9
Keywords
- Variable exponent
- Maximal monotone operator
- Renormalized solution
- Generalized Sobolev spaces
- Neumann boundary condition