Ahmed Youssfi, Mohamed Mahmoud Ould Khatri
Abstract:
We prove a continuous embedding that allows us to obtain a boundary trace imbedding
result for anisotropic Musielak-Orlicz spaces, which we then apply to obtain an
existence result for Neumann problems with nonlinearities on the boundary associated
to some anisotropic nonlinear elliptic equations in Musielak-Orlicz spaces constructed
from Musielak-Orlicz functions on which and on their conjugates we do not assume the
Δ2-condition. The uniqueness of weak solutions is also studied.
Submitted April 12, 2019. Published April 5, 2021.
Math Subject Classifications: 46E35, 35J20, 35J25, 35B38, 35D30.
Key Words: Musielak-Orlicz space; imbedding; boundary trace imbedding;
weak solution; minimizer.
DOI: https://doi.org/10.58997/ejde.2021.26
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Ahmed Youssfi University Sidi Mohamed Ben Abdellah Laboratory of Mathematical Analysis and Applications National School of Applied Sciences P.O. Box 72 Fès-Principale, Fez, Morocco email: ahmed.youssfi@usmba.ac.ma, ahmed.youssfi@gmail.com |
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Mohamed Mahmoud Ould Khatri University Sidi Mohamed Ben Abdellah National School of Applied Sciences P.O. Box 72 Fès-Principale, Fez, Morocco email: mahmoud.ouldkhatri@usmba.ac.ma |
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