On the structure of Hardy–Sobolev–Maz'ya inequalities

By Stathis Filippas, A. Tertikas, J. Tidblom. 2008

60 citations recorded by the source corpus.

We establish new improvements of the optimal Hardy inequality in the half-space. We first add all possible linear combinations of Hardy type terms, thus revealing the structure of this type of inequalities and obtaining best constants. We then add the critical Sobolev term and obtain necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya type inequalities.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/ffec12bb96a74b8ae113aac787541c0c0ef6971b

Citations in the corpus

• Sharp Poincar\'e-Hardy and Poincar\'e-Rellich inequalities on the hyperbolic space (2015, unknown): “efore stating it, we recall that the constant 1/4 in the Hardy-Maz’ya inequality Z R+ Z RN−1 |∇v|2 dxdy≥ 1 4 Z R+ Z RN−1 v2 y2 dxdy, where (x,y) ∈ RN−1 ×R+, is sharp, see [29, 2.1.6, Cor. 3] and also [19, 21]. Corollary 2.3. Let N≥ 3.For all v∈ C∞ c (RN +) the following inequality holds (2.5) Z R+ Z”