On Sobolev spaces and density theorems on Finsler manifolds

Document Type : Original Article

Authors

Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Ave., Tehran 15914, Iran

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 H1p(M). As a consequence, the weak solutions u of the Dirichlet equation Δu=f can be approximated by C∞ functions with compact support on M. Moreover, let W⊆M be a regular domain with the Cr boundary ∂W, then the set of all real functions in Cr(W)∩C0(W―) is dense in Hkp(W), where k≤r. Finally, several examples are illustrated and sharpness of the inequality k≤r is shown.

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References

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AUT Journal of Mathematics and Computing
Volume 1, Issue 1
February 2020
Pages 37-45

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