Hardy inequalities with optimal constants and remainder terms

By Filippo Gazzola, Hans-Christoph Grunau, Enzo Mitidieri. 2003

153 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/167bb5377188674ef5eda829dbb8c639ad59cd1f

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In Applied Mathematics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Sharp Poincar\'e-Hardy and Poincar\'e-Rellich inequalities on the hyperbolic space (2015, background): “without any claim for completeness [6, 12, 16, 22, 23, 33, 39].”
Semilinear elliptic equations for the fractional Laplacian with Hardy potential (2011, background): “We also quote [3], [44], [26] for related improvements.”
Some Hardy Inequalities on the Heisenberg Group (2004, methodology): “The preceding theorems can be generalized to the case of the degree p � 2, just as in [ 14 ].”
Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on $ {\Bbb R}^n $ (2001, background): “This kind of problems have their root in the investigation of certain Hardy type inequalities [BC], [BV], [DH], [ GGM ], [M2].”
Best Constants in the Hardy-Rellich Inequalities and Related Improvements (2006, methodology): “in particular that improved Hardy inequalities arise in the study of singular solutions of the Gelfand problem [BT, BV], whereas the improved Rellich in the biharmonic analogue of the Gelfand problem [GGM]. It is worth noting the work of Eilertsen [E] which is connected with the work of Maz’ya [M2] ”
Series expansion for L^p Hardy inequalities (2003, methodology): “For other types of improved Hardy inequalities we refer to [BV, GGM , M, VZ]; in all these works one correction term is added in the right hand side of the plain Hardy inequality.”
Pitt’s inequality with sharp convolution estimates (2006, background): “Considerable interest has been given recently to the study of Hardy, Rellich and weighted Sobolev inequalities on complete Riemannian manifolds with optimal constants and remainder terms (for example, see [1], [10], [13]).”
Optimal Hardy–Rellich inequalities, maximum principle and related eigenvalue problem (2006, unknown): “[11] proved that for n 5 there exist C,C1 > 0 such that for all u ∈ H 2 0 (Ω) or u ∈ H 2(Ω) ∩ H 1 0 (Ω), the following inequality holds, ∫”
Hardy-type inequalities related to degenerate elliptic differential operators (2006, background): “holds for every ξ, η, s ∈ R with ξ > 0, ξ > η and s ≥ 1 (see [31]).”
Hardy inequalities on Riemannian manifolds and applications (2012, background): “holds for every ξ, η, s ∈ R, with ξ > 0, ξ > η and s 1 (see [27]).”
Rellich inequalities with weights (2011, background): “6) under some restrictions on α (see also [3], [10], [11] and [12] for related results).”