Abstract Consider Hardy s inequalities with general weight φ for functions nonzero on the boundary. By an integral identity in C1(),define Hilbert spaces H1k(Ω, φ) called Sobolev-Hardy spaces with weight φ. As a corollary of this identity, Hardy s inequalities with weight φ in C1() follow. At last, by Hardy s inequalities with weight φ = 1, discuss the eigenvalue problem of the Laplace-Hardy operator with critical parameter (N - 2)2/4 in H11(Ω).
Issue Date: 05 June 2007
Cite this article:
CHEN Zhihui,SHEN Yaotian. General Hardy’s inequalities for functions nonzero on the boundary[J]. Front. Math. China,
2007, 2(2): 169-181.
),define Hilbert spaces H1k(Ω, φ) called Sobolev-Hardy spaces with weight φ. As a corollary of this identity, Hardy s inequalities with weight φ in C1(
) follow. At last, by Hardy s inequalities with weight φ = 1, discuss the eigenvalue problem of the Laplace-Hardy operator with critical parameter (N - 2)2/4 in H11(Ω).