Sobolev Spaces in Metric Spaces

https://doi.org/10.55276/ljs.v24i1.96

Authors

  • Zohra Farnana

Keywords:

Newtonian functions; doubling measure; metric space; nonlinear; Sobelev spaces; Poincaré inequality.

Abstract

We study Sobolev type spaces (called Newtonian spaces) in metric measure spaces equipped with a doubling measure and supporting a p −Poincaré inequality. The Sobolev spaces are defined using the minimal upper gradient which is a substitute of the modulus of the usual gradient. We show that they are the right extension of the usual Sobolev spaces in Rn . In particular Newtonian functions are quasicontinuous and that they are absolutely continues on almost every curve. Moreover, Newtonian functions are continuous on the complement of small sets.

Published

2021-04-27

How to Cite

Farnana, Z. (2021) “Sobolev Spaces in Metric Spaces”, The Libyan Journal of Science, 24(1), pp. 79–88. doi: 10.55276/ljs.v24i1.96.

Issue

Section

Mathematics
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