Existence of weak solutions to borderline double-phase problems with logarithmic convection term
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911747144679424 |
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| author | Tran, Minh-Phuong Nguyen, Thanh-Nhan |
| author_facet | Tran, Minh-Phuong Nguyen, Thanh-Nhan |
| contents | In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data. The proof is based on the surjectivity theorem for the pseudo-monotone operators and modular function spaces and embedding theorems in generalized Orlicz spaces. Our approach in this paper can be extended naturally to a larger class of unbalanced double-phase problems with logarithmic perturbation and gradient dependence on the right-hand sides. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_06700 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence of weak solutions to borderline double-phase problems with logarithmic convection term Tran, Minh-Phuong Nguyen, Thanh-Nhan Analysis of PDEs Functional Analysis In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data. The proof is based on the surjectivity theorem for the pseudo-monotone operators and modular function spaces and embedding theorems in generalized Orlicz spaces. Our approach in this paper can be extended naturally to a larger class of unbalanced double-phase problems with logarithmic perturbation and gradient dependence on the right-hand sides. |
| title | Existence of weak solutions to borderline double-phase problems with logarithmic convection term |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2309.06700 |