Estimation optimale du gradient du semi-groupe de la chaleur sur le ...

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506 J. Van Schaftingen / Journal of Functional Analysis 236 (2006) 490–516 Proposition 4.6. If 1 ℓ n, then if and only if 1 k
J. Van Schaftingen / Journal of Functional Analysis 236 (2006) 490–516 507 Corollary 4.9. (Bourgain and Brezis [3]) Let f ∈ L1 (R2 ; R2 ).Ifdiv f = 0 in the sense of distributions, then log 1 |x| ∗ f ∈ L∞R 2 ; R 2 . Other interesting examples can be obtained in a similar way: Proposition 4.10. If 1 ℓ n and 0
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Journal of Functional Analysis 236
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H.-Q. Li / Journal of Functional An
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x(s) = H.-Q. Li / Journal of Functi
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et et Donc, H.-Q. Li / Journal of F
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et Posons H.-Q. Li / Journal of Fun
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⎛ ⎜ ⎝ − H.-Q. Li / Journal
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Donc, H.-Q. Li / Journal of Functio
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5. Quelques problèmes ouverts H.-Q
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D. Kucerovsky / Journal of Function
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D. Serre / Journal of Functional An
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The assumption tells us that the fo
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3.4. The zeroes of ( √ z, η) D.
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4.1. Persistence of surface waves D
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When G = η ⊗ r, we obtain Becaus
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This polynomial satisfies D. Serre
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A. Wi´snicki / Journal of Function
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A. Wi´snicki / Journal of Function
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Therefore, A. Wi´snicki / Journal
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Page 91 and 92: H. Schultz / Journal of Functional
Page 121 and 122: we now have (cf. (7.8)) that H. Sch
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Page 127 and 128: 2.2. Definition J. Van Schaftingen
Page 135 and 136: Since ϕ = ϕ0 + ϕ1 ∧ ωN, one h
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Page 151 and 152: A. Olofsson / Journal of Functional
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Page 187 and 188: 3. The Poisson transform K. Koufany
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K. Koufany, G. Zhang / Journal of F
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Its limit when t → 0is K. Koufany
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and K. Koufany, G. Zhang / Journal
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A. Porretta, L. Véron / Journal of
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L. Miller / Journal of Functional A
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1.2. Spectral and growth bounds L.
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By duality, Kp,T is also defined by
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E. Kissin / Journal of Functional A
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Using it, we obtain as in (3.2) tha
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5. Structure of the group ZS E. Kis
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M.J. Crabb / Journal of Functional
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M.J. Crabb / Journal of Functional
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S. Albeverio, A. Kosyak / Journal o
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The minimum is realized for S. Albe
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For m = 3wehave S. Albeverio, A. Ko
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hence S. Albeverio, A. Kosyak / Jou
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φpq(t; tqq) = Since = S. Albeveri
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hence C = C3 = S. Albeverio, A. Kos
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and S. Albeverio, A. Kosyak / Journ
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D. Brydges, A. Talarczyk / Journal
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Furthermore, D. Brydges, A. Talarcz
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D. Bucur / Journal of Functional An
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lim n→∞ Ω lim sup n→∞
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