General Hardy’s inequalities for functions nonzero on the boundary

doi:10.1007/s11464-007-0012-7

PDF(200 KB)

Front. Math. China ›› 2007, Vol. 2 ›› Issue (2) : 169-181. DOI: 10.1007/s11464-007-0012-7

General Hardy’s inequalities for functions nonzero on the boundary

CHEN Zhihui, CHEN Zhihui, SHEN Yaotian, SHEN Yaotian

Author information +

History +

Abstract

Consider Hardy s inequalities with general weight φ for functions nonzero on the boundary. By an integral identity in C¹(

),define Hilbert spaces H¹_k(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).

Cite this article

EndNote

Ris (Procite)

Bibtex

Download citation ▾

CHEN Zhihui, CHEN Zhihui, SHEN Yaotian, SHEN Yaotian. General Hardy’s inequalities for functions nonzero on the boundary. Front. Math. China, 2007, 2(2): 169‒181 https://doi.org/10.1007/s11464-007-0012-7