Alexander A. Balinsky W. Desmond Evans Roger T. Lewis Page 1 Universitext Alexander A.
Balinsky W. Desmond Evans Roger T. Lewis The Analysis and Geometry of Hardy's …

For a general subcritical second-order elliptic operator P in a domain Ω⊂ R n (or
noncompact manifold), we construct Hardy-weight W which is optimal in the following sense …

The fractional Sobolev spaces studied in the book were introduced in the 1950s by
Aronszajn, Gagliardo and Slobodeckij in an attempt to fill the gaps between the classical …

We establish in this paper general geometric Hardy's identities and inequalities on domains
in RN in the spirit of their celebrated works by Brezis-Vázquez and Brezis-Marcus. Hardy's …

In this paper we obtain an inequality on the unit disk B in R2, which improves the classical
Moser–Trudinger inequality and the classical Hardy inequality at the same time. Namely …

In this work we establish trace Hardy and trace Hardy–Sobolev–Maz'ya inequalities with
best Hardy constants for domains satisfying suitable geometric assumptions such as mean …

We present upper and lower bounds for Steklov eigenvalues for domains in RN C1 with C2
boundary compatible with the Weyl asymptotics. In particular, we obtain sharp upper bounds …

We prove sharp homogeneous improvements to L 1 weighted Hardy inequalities involving
distance from the boundary. In the case of a smooth domain, we obtain lower and upper …

We present a generic functional inequality on Riemannian manifolds, both in additive and
multiplicative forms, that produces well known and genuinely new Hardy-type inequalities …

Firstly, this paper establishes useful forms of the remainder term of Hardy-type inequalities
on general domains where the weights are functions of the distance to the boundary. For …