【摘 要】
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This paper is devoted to the study of the subspace of Wm'r of functions that vanish on a part γ0 of the boundary.The author gives a crucial estimate of the Poi
【机 构】
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Laboratoire Analyse et Probabitilités
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This paper is devoted to the study of the subspace of Wm'r of functions that vanish on a part γ0 of the boundary.The author gives a crucial estimate of the Poincaré constant in balls centered on the boundary of γ0.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 γ0,in this subspace.The result is first proved for m =1,then generalized to the case where m ≥ 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 γ0,namely that it is locally the graph of some Lipschitz-continuous function.
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