Optimizing Improved Hardy Inequalities

By Stathis Filippas, A. Tertikas. 2002

215 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b1191ef35b685b788667dcfd079567c9d83968ce

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In Applied Mathematics

Citations in the corpus

Sharp Two–Sided Heat Kernel Estimates for Critical Schrödinger Operators on Bounded Domains (2006, background): “heorem 2.10. 3.1 Boundary upper bounds and complete sharp description of the heat kernel for large values of time We ﬁrst recall the following improved Hardy-Sobolev inequality stated in Theorem A in [FT] (see also inequality (3.3) in [BFT2]) Proposition 3.1 For N ≥ 3, let Ω ⊂ RN be a smooth bounded”
On the best constant of Hardy―Sobolev inequalities (2009, methodology): “We next consider the k‐improved Hardy‐Sobolev inequality derived in [ FT ].”
Sharp Hardy–Sobolev inequalities (2004, unknown): “([5], Theorem A) ∫”
Sharp uncertainty principles on Riemannian manifolds: the influence of curvature (2013, background): “[5] G. Barbatis, S. Filippas, A. Tertikas, A unified approach to improved Lp Hardy inequalities with best constants.”
A geometric characterization of a sharp Hardy inequality (2011, unknown): “In the case p = 2, Brezis and Marcus [7] proved the following inequality for bounded domains with C2 boundary (1.8) ∫ Ω |∇u|2dx ≥ 1 4 ∫ Ω (u/δ)2dx+ Λ ∫ Ω u2dx,∀u ∈ H10 (Ω), where Λ is the best constant defined as (1.9) Λ := inf∫ Ω f 2dx=1 [ ∫ Ω |∇f |2dx− 1 4 ∫ Ω f2 δ2 dx ] .”
Sharp Poincar\'e-Hardy and Poincar\'e-Rellich inequalities on the hyperbolic space (2015, background): “alls. Before giving a precise statement, we ﬁrst introduce some auxiliary functions, which are basically the iterated log functions arising in several paper in the euclidean setting, see for instance [20]. Let X1(t) = (1 − logt)−1 for t∈ (0,1].We deﬁne recursively the functions: Xk(t) = X1(Xk−1(t)),”
Optimal Hardy–Rellich inequalities, maximum principle and related eigenvalue problem (2006, background): “On the lines of improving Hardy–Sobolev inequality for functions in H 1 0 (Ω) (see [1,3,6,8,10]) there has been a considerable interest in improving (1.”
On a question of Brezis and Marcus (2006, unknown): “[BV], [BM], [BFT], [DD], [HHL], [ FT ],[M], [VZ], [T], and references therein.”
A ground state alternative for singular Schrodinger operators (2004, background): “As it is noted in [7], attainment in the standard Sobolev space of the best constant in the Hardy inequality, or in the Hardy inequality with a further corrected potential cannot serve as a criterion for the nonexistence of a weighted spectral gap.”
Bessel pairs and optimal Hardy and Hardy–Rellich inequalities (2011, background): “has a positive solution on (0, R). Such a function W will be called a Bessel potential on (0, R). This type of characterization was established recently by the authors [20] in the case where a = 0, yielding in particular the recent improvements of Hardy’s inequalities (on bounded domains) establishe”
On existence of minimizers for the Hardy–Sobolev–Maz’ya inequality (2005, background): “Then one has ([16], Theorem A) the following analog of (2):”
Series expansion for L^p Hardy inequalities (2003, methodology): “On the other hand, when p = 2 and K = {0} the full series was obtained in [ FT ] by a dierent method.”
OPTIMAL HARDY WEIGHT FOR SECOND-ORDER ELLIPTIC OPERATOR: AN ANSWER TO A PROBLEM OF AGMON (2012, background): “Indeed, it is known [4, 48, 49] that P − λ0W is always critical when property (b) does not hold (see also [23]).”
Estimates for the optimal constants in multipolar Hardy inequalities for Schrödinger and Dirac operators (2008, background): “See [22, 12] for more details and further references.”