On some Elliptic and Parabolic Problems Involving the Anisotropic $p(u)$-Laplacian
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912651995512832 |
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| author | Bal, Kaushik Gupta, Shilpa |
| author_facet | Bal, Kaushik Gupta, Shilpa |
| contents | We investigate a class of elliptic and parabolic partial differential equations driven by p(u) laplacian. This dependence necessitates the use of variable exponent Sobolev spaces specifically tailored to the anisotropic framework. For the elliptic case, we establish the existence of a weak solution by employing the theory of pseudomonotone operators in conjunction with suitable approximation techniques. In the parabolic setting, the existence of a weak solution is obtained via a time discretization scheme and Schauder fixed-point theorem, supported by a priori estimates and compactness arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On some Elliptic and Parabolic Problems Involving the Anisotropic $p(u)$-Laplacian Bal, Kaushik Gupta, Shilpa Analysis of PDEs We investigate a class of elliptic and parabolic partial differential equations driven by p(u) laplacian. This dependence necessitates the use of variable exponent Sobolev spaces specifically tailored to the anisotropic framework. For the elliptic case, we establish the existence of a weak solution by employing the theory of pseudomonotone operators in conjunction with suitable approximation techniques. In the parabolic setting, the existence of a weak solution is obtained via a time discretization scheme and Schauder fixed-point theorem, supported by a priori estimates and compactness arguments. |
| title | On some Elliptic and Parabolic Problems Involving the Anisotropic $p(u)$-Laplacian |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.14432 |