Sharp Fractional Hardy Inequalities in Half-Spaces

By Rupert L. Frank, Robert Seiringer. 2009

63 citations recorded by the source corpus.

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces on half-spaces. Our proof relies on a nonlinear and nonlocal version of the ground state representation.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5400525b823c41c09767ad39a47404882cd52666

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Nguyen Huong Lam
2. G. Lu
3. Lu Zhang
4. Antti V. Vahakangas
5. Bartłomiej Dyda
6. Rupert L. Frank
7. Caifeng Zhang
8. Hanli Tang

In Mathematical Physics

1. Nguyen Huong Lam
2. G. Lu
3. Bartłomiej Dyda
4. Rupert L. Frank
5. Hanli Tang
6. Caifeng Zhang
7. Y. Yang

Citations in the corpus

• Fractional Hardy-Sobolev-Maz'ya inequality for domains (2011, methodology): “This constant is independent of Ω and coincides with that on the halfspace which was earlier found in [3, 9].”
• The best constant in a fractional Hardy inequality (2008, unknown): “Fractional Hardy inequalities with optimal constants for different domains were derived in [6, 3, 7, 5, 9].”
• Factorizations and Hardy’s type identities and inequalities on upper half spaces (2019, background): “We note here that a sharp version of the Hardy inequality for fractional Sobolev spaces on half-spaces was investigated in [22].”
• A framework for fractional Hardy inequalities (2013, background): “In [9] these results are further refined; let us also mention the other related papers [4, 8, 11, 12, 34].”