@article {
author = {Bidabad, Behrooz and Shahi, Alireza},
title = {On Sobolev spaces and density theorems on Finsler manifolds},
journal = {AUT Journal of Mathematics and Computing},
volume = {1},
number = {1},
pages = {37-45},
year = {2020},
publisher = {Amirkabir University of Technology},
issn = {},
eissn = {},
doi = {10.22060/ajmc.2018.3039},
abstract = {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∞ 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 ∆u = f can be approximated by C∞ functions with compact support on M. Moreover, let W ⊂ M be a regular domain with the C r boundary ∂W, then the set of all real functions in C r (W) ∩ C 0 (W) is dense in H p k (W), where k ≤ r. Finally, several examples are illustrated and sharpness of the inequality k ≤ r is shown},
keywords = {Density theorem,Sobolev spaces,Dirichlet problem,Finsler space},
url = {https://ajmc.aut.ac.ir/article_3039.html},
eprint = {https://ajmc.aut.ac.ir/article_3039_ef823186580a9c859620d42c8543c999.pdf}
}