TY - JOUR
ID - 3039
TI - On Sobolev spaces and density theorems on Finsler manifolds
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN -
AU - Bidabad, Behrooz
AU - Shahi, Alireza
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
AD - Faculty of Mathematics and computer science, Amirkabir University of Technology
Y1 - 2020
PY - 2020
VL - 1
IS - 1
SP - 37
EP - 45
KW - Density theorem
KW - Sobolev spaces
KW - Dirichlet problem
KW - Finsler space
DO - 10.22060/ajmc.2018.3039
N2 - 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
UR - https://ajmc.aut.ac.ir/article_3039.html
L1 - https://ajmc.aut.ac.ir/article_3039_ef823186580a9c859620d42c8543c999.pdf
ER -