%0 Journal Article
%T On Sobolev spaces and density theorems on Finsler manifolds
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z
%A Bidabad, Behrooz
%A Shahi, Alireza
%D 2020
%\ 02/01/2020
%V 1
%N 1
%P 37-45
%! On Sobolev spaces and density theorems on Finsler manifolds
%K Density theorem
%K Sobolev spaces
%K Dirichlet problem
%K Finsler space
%R 10.22060/ajmc.2018.3039
%X 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
%U https://ajmc.aut.ac.ir/article_3039_ef823186580a9c859620d42c8543c999.pdf