Topics from spectral theory of differential operators

Hinz, Andreas M.

doi:10.1090/conm/340/06114

Cited by 5 publications

(5 citation statements)

References 55 publications

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“…This implies by (11)- (14) and (16) that e n L ∞ ≤ const.λ N /4 n . Therefore the conclusion follows from the estimate c 1 n 2/N ≤ λ n ≤ c 2 n 2/N for all n ∈ N (see, e.g., Davies [9, Theorem 6.3.1]).…”

Section: Introductionmentioning

confidence: 65%

L ∞-estimates for Sobolev functions in terms of ∇ and Δ

Okazawa

2008

Math. Z.

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Several L ∞ -estimates are obtained for u ∈ C m c (R N ) in terms of k u L p and ∇( l u) L p , where k, l ∈ N ∪ {0} are determined by m. If p = 2, then the estimates are given with explicit constants. However, if p = 2, it is difficult to derive explicit constants except in two simple cases. Applicability to PDE's is illustrated.with suitable α depending on m, p and N . The validity of this type of inequalities (with p = 2) has been pointed out by Temam in his book [28, p. 52]. He calls them Agmon's inequalities and cites [2]; actually, in [28] the whole space R N is replaced with a bounded domain .Agmon's inequalities in the sense of [28] are divided into two cases depending on the spatial dimension N . Taylor [27, Sect. 13.3] has proved them for testing functions. Namely, N. Okazawa (B)

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Section: Introductionmentioning

confidence: 65%

L ∞-estimates for Sobolev functions in terms of ∇ and Δ

Okazawa

2008

Math. Z.

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“…3,5], [16,17,18,21,24,26,27,28,29,30,31,32,33,34,35,36,38,40,47,49,50], [51,Chs. 2,6,7], [59,60,70,71,72,73,75,76,80,82,83], [87, Sect. 2.7], [88,89,90,94,95,96,97].…”

Section: Power-weighted Birman-hardy-rellich-type Inequalities With L...mentioning

confidence: 99%

A Sequence of Weighted Birman-Hardy-Rellich Inequalities with Logarithmic Refinements

Gesztesy¹,

Littlejohn²,

Michael³

et al. 2020

Preprint

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“…3,5], [16,17,18,21,23,25,26,27,28,29,31,32,33,34,35,36,37,39,44,46,47], [48,Chs. 2,6,7], [56,57,65,66,67,68,70,71,74,76,77], [81,Sect. 2.7], [82,83,84,88,89,90,91].…”

Section: Introduction and Notations Employedmentioning

confidence: 99%