Academic Journal
On Sobolev spaces and density theorems on Finsler manifolds
| العنوان: | On Sobolev spaces and density theorems on Finsler manifolds |
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| المؤلفون: | Behroz Bidabad, Alireza Shahi |
| المصدر: | AUT Journal of Mathematics and Computing, Vol 1, Iss 1, Pp 37-45 (2020) |
| بيانات النشر: | Amirkabir University of Technology, 2020. |
| سنة النشر: | 2020 |
| المجموعة: | LCC:Mathematics |
| مصطلحات موضوعية: | density theorem, sobolev spaces, dirichlet problem, finsler space, Mathematics, QA1-939 |
| الوصف: | Here, a natural extension of Sobolev spaces is defined for a Finsler structure $F$ and it is shown that the set of all real $C^{\infty}$ functions with compact support on a forward geodesically complete Finsler manifold $(M, F),$ is dense in the extended Sobolev space $H^p_1(M)$. As a consequence, the weak solutions u of the Dirichlet equation $\Delta u=f$ can be approximated by $C^{\infty}$ functions with compact support on $M$. Moreover, let $W\subseteq M$ be a regular domain with the $C^r$ boundary $\partial W$, then the set of all real functions in $C^r(W)\cap C^0(\overline{W})$ is dense in $H^p_k(W)$, where $k\leq r$. Finally, several examples are illustrated and sharpness of the inequality $k\leq r$ is shown. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 2783-2449 2783-2287 |
| Relation: | https://ajmc.aut.ac.ir/article_3039_bcbcb1f45609881ba462e01ecc38e982.pdf; https://doaj.org/toc/2783-2449; https://doaj.org/toc/2783-2287 |
| DOI: | 10.22060/ajmc.2018.3039 |
| URL الوصول: | https://doaj.org/article/68b3810b2b8745d4b57d95ebf177794f |
| رقم الانضمام: | edsdoj.68b3810b2b8745d4b57d95ebf177794f |
| قاعدة البيانات: | Directory of Open Access Journals |
| تدمد: | 27832449 27832287 |
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| DOI: | 10.22060/ajmc.2018.3039 |