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The Dirichlet Energy Integral and Variable Exponent Sobolev Spaces with Zero Boundary Values |
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| Authors: | Petteri Harjulehto Peter Hästö Mika Koskenoja Susanna Varonen |
| Affiliation: | (1) Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014 Helsinki, Finland;(2) Department of Mathematical Sciences, NTNU, 7491 Trondheim, Norway |
| Abstract: | We define and study variable exponent Sobolev spaces with zero boundary values. This allows us to prove that the Dirichlet energy integral has a minimizer in the variable exponent case. Our results are based on a Poincaré-type inequality, which we prove under a certain local jump condition for the variable exponent. |
| Keywords: | variable exponent Sobolev space zero boundary values Sobolev capacity Poincaré inequality Dirichlet energy integral |
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