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

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706 D. Brydges, A. Talarczyk / Journal of Functional Analysis 236 (2006) 682–711 Proposition 4.6. Assume that d = 1, Λ = (a, b), B = c(x) d , where c is twice continuously dx differentiable and c2 (x) const > 0. Let s denote the scale function of the diffusion process generated by −B ′ B. Then the kernel of the operator AL is of the form: ⎧ s(y)−s(a) 2L(s(x)−s(a)) s(b)−s(y) for a
D. Brydges, A. Talarczyk / Journal of Functional Analysis 236 (2006) 682–711 707 which coincides with (4.23). If b − a
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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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Therefore, A. Wi´snicki / Journal
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H. Schultz / Journal of Functional
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we now have (cf. (7.8)) that H. Sch
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J. Van Schaftingen / Journal of Fun
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2.2. Definition J. Van Schaftingen
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Since ϕ = ϕ0 + ϕ1 ∧ ωN, one h
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K. Koufany, G. Zhang / Journal of F
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3. The Poisson transform K. Koufany
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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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S. Albeverio, A. Kosyak / Journal o
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The minimum is realized for S. Albe
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Page 289 and 290: For m = 3wehave S. Albeverio, A. Ko
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Page 301 and 302: hence C = C3 = S. Albeverio, A. Kos
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