Amirkabir University of TechnologyAUT Journal of Mathematics and Computing1120200201On Sobolev spaces and density theorems on Finsler manifolds3745303910.22060/ajmc.2018.3039ENBehroozBidabadDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)0000-0003-3993-4268AlirezaShahiFaculty of Mathematics and computer science, Amirkabir University of TechnologyJournal Article20180403Here, a natural extension of Sobolev spaces is defined for a Finsler structure F and it is shown that the set of all real C<sup>∞</sup> functions with compact support on a forward geodesically complete Finsler manifold (M, F), is dense in the extended Sobolev space H <sup>p</sup> <sub>1</sub> (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 <sup>r</sup> (W) ∩ C <sup>0</sup> (W) is dense in H <sup>p</sup> <sub>k</sub> (W), where k ≤ r. Finally, several examples are illustrated and sharpness of the inequality k ≤ r is shownhttps://ajmc.aut.ac.ir/article_3039_ef823186580a9c859620d42c8543c999.pdf