On Some Generalisations of Meyers-Serrin Theorem

Authors

  • Davide Guidetti University of Bologna
  • Batu Güneysu Humboldt-Universität zu Berlin
  • Diego Pallara Università del Salento

DOI:

https://doi.org/10.6092/issn.2240-2829/5894

Keywords:

Meyers-Serrin theorem, Differential operators on manifolds, Vector bundles

Abstract

We present a generalisation of Meyers-Serrin theorem, in which we replace the standard weak derivatives in open subsets of ℝm with finite families of linear differential operators defined on smooth sections of vector bundles on a (not necessarily compact) manifold X.

References

A.V. Balakrishnan, Applied Functional Analysis, Applications of Mathematics 3, Springer-Verlag (1976).

G. B. Folland, ”Subelliptic estimates and function spaces on nilpotent Lie groups”, Ark. Mat. 13 (1975), 161-207.

B. Franchi, R. Serapioni, F. Serra Cassano, ”Meyers-Serrin type theorems and relaxation of variational integrals depending on vector fields”, Houston J. Math. 22 (1996), 859-890.

B. Franchi, R. Serapioni, F. Serra Cassano, ”Approximation and imbedding theorems for weighted Sobolev spaces associated with Lipschitz continuous vector fields”, Boll. Un. Mat. It. B 7 (1997), 83-117.

D. Guidetti, B. Güneysu, D. Pallara, ”L1 −elliptic regularity and H = W on the whole Lp −scale on arbitrary manifolds”, Preprint.

E. Hebey, Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities, Lecture Notes 5, American Mathematical Society Courant Institute of Mathematical Sciences (2000).

N.G. Meyers, J. Serrin, ”H = W”, Proc. Nat. Acad. Sci. U.S.A 51 (1964), 1055-1056.

L.I. Nicolaescu, Lectures on the geometry of manifolds, World Scientific Publishing Co., (1996), 2 nd Edition (2007).

R. O. Wells, Differential analysis on complex manifolds, Springer Graduete Texts in Mathematics 65 (1979).

Downloads

Published

2015-12-28

How to Cite

Guidetti, D., Güneysu, B., & Pallara, D. (2015). On Some Generalisations of Meyers-Serrin Theorem. Bruno Pini Mathematical Analysis Seminar, 6(1), 116–127. https://doi.org/10.6092/issn.2240-2829/5894

Issue

Seminars 2015

Section

Articles

License

Copyright (c) 2015 Davide Guidetti, Batu Güneysu, Diego Pallara

Copyrights and publishing rights of all the texts on this journal belong to the respective authors without restrictions.

Creative Commons License

This journal is licensed under a Creative Commons Attribution 4.0 International License. (full legal code)
See also our Open Access Policy.