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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.01783 |
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| _version_ | 1866912566182150144 |
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| author | Barbara, Abdelkrim Bousmaha, Ahmed Shimi, Mohammed |
| author_facet | Barbara, Abdelkrim Bousmaha, Ahmed Shimi, Mohammed |
| contents | In this paper, we prove a new continuous embedding theorem for fractional Sobolev spaces with variable exponents into variable exponent Lebesgue spaces on unbounded domains. As an application, we study a class of nonlocal elliptic problems driven by the fractional $p(x, \cdot)$-Laplacian operator. Using variational methods combined with the established embedding result, we prove the existence of nontrivial weak solutions under suitable growth and regularity conditions on the nonlinearity.\\ A significant analytical challenge addressed in this work arises from both the nonlocal behavior of the fractional $p(x, \cdot)$-Laplacian and the lack of compactness induced by the unboundedness of the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embedding Results and Fractional $p(x,.)$-Laplacian Problem in Unbounded Domains Barbara, Abdelkrim Bousmaha, Ahmed Shimi, Mohammed Analysis of PDEs In this paper, we prove a new continuous embedding theorem for fractional Sobolev spaces with variable exponents into variable exponent Lebesgue spaces on unbounded domains. As an application, we study a class of nonlocal elliptic problems driven by the fractional $p(x, \cdot)$-Laplacian operator. Using variational methods combined with the established embedding result, we prove the existence of nontrivial weak solutions under suitable growth and regularity conditions on the nonlinearity.\\ A significant analytical challenge addressed in this work arises from both the nonlocal behavior of the fractional $p(x, \cdot)$-Laplacian and the lack of compactness induced by the unboundedness of the domain. |
| title | Embedding Results and Fractional $p(x,.)$-Laplacian Problem in Unbounded Domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.01783 |