on sobolev spaces and density theorems on finsler manifolds

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