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| Density Results in Sobolev Spaces Whose Elements Vanish on a Part of the Boundary |
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Citation： |
Jean-Marie Emmanuel BERNARD.Density Results in Sobolev Spaces Whose Elements Vanish on a Part of the Boundary[J].Chinese Annals of Mathematics B,2011,32(6):823~846 |
| Page view： 1846
Net amount： 1485 |
Authors： |
Jean-Marie Emmanuel BERNARD; |
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| Abstract： |
This paper is devoted to the study of the subspace of
$W^{m,r}$ of functions that vanish on a part $\g_0$ of the
boundary. The author gives a crucial estimate of the Poincar\'e constant in
balls centered on the boundary of $\g_0$. Then, the
convolution-translation method, a variant of the standard mollifier
technique, can be used to prove the density of smooth functions that
vanish in a neighborhood of $\g_0$, in this subspace. The result is
first proved for $m=1$, then generalized to the case where $m\ge 1$,
in any dimension, in the framework of Lipschitz-continuous
domain. However, as may be expected, it is needed to make additional
assumptions on the boundary of $\g_0$, namely that it is locally
the graph of some Lipschitz-continuous function. |
Keywords： |
Density results, Boundary value problems, Sobolev spaces |
Classification： |
41A30, 35A99, 35G15 |
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