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Analysis and Mathematical Physics

, Volume 8, Issue 2, pp 289–308 | Cite as

A \(\texttt {p}(\cdot )\)-Poincaré-type inequality for variable exponent Sobolev spaces with zero boundary values in Carnot groups

  • Thomas BieskeEmail author
  • Robert D. Freeman
Article
  • 59 Downloads

Abstract

We prove a \(\texttt {p}(\cdot )\)-Poincaré-type inequality for variable exponent Sobolev spaces with zero boundary values in Carnot groups. We then establish the existence and uniqueness (up to a set of zero \(\texttt {p}(\cdot )\)-capacity) of a minimizer to the Dirichlet energy integral for the variable exponent case.

Keywords

Poincaré inequality Sobolev spaces with zero boundary values Dirichlet energy minimizer 

Mathematics Subject Classification

Primary 46E35 35J66 53C17 31C45 35H20 Secondary 22E25 31E05 

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA

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