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| A Poincar′e Inequality in a Sobolev Space with a Variable Exponent |
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Citation： |
Philippe G. CIARLET,George DINCA.A Poincar′e Inequality in a Sobolev Space with a Variable Exponent[J].Chinese Annals of Mathematics B,2011,32(3):333~342 |
| Page view： 1705
Net amount： 1652 |
Authors： |
Philippe G. CIARLET; George DINCA; |
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| Abstract： |
Let $\Omega$ be a domain in $\mathbb{R}^N$. It is shown that a
generalized Poincar\'{e} inequality holds in cones contained in the
Sobolev space $W^{1,p(\cdot)}(\Omega)$, where $p(\cdot) : \overline
\Omega \to[1,\infty[$ is a variable exponent. This inequality is itself
a corollary to a more general result about equivalent norms
over such cones. The approach in this paper avoids the difficulty arising from the
possible lack of density of the space $\mathcal{D}(\Omega)$ in the
space $\{v\in W^{1,p(\cdot)}(\Omega) ; \mathop{\mathrm{tr}} v = 0
\text{ on } \partial \Omega\}$. Two applications are also discussed. |
Keywords： |
Poincar′e inequality, Sobolev spaces with variable exponent |
Classification： |
26D10, 26D15, 46E30, 46E35 |
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