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

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662 S. Albeverio, A. Kosyak / Journal of Functional Analysis 236 (2006) 634–681 where D(t) = diag(t21,...,tp1; t32,...,tp2; t43,...,tp3; ...; tpp−1). We have <strong>de</strong>t C1(t) = 1 + p r=1 1i1
hence S. Albeverio, A. Kosyak / Journal of Functional Analysis 236 (2006) 634–681 663 Using the <strong>la</strong>tter inequality we get (see (48)) M 12...p−1 12...p 12...p−1 (Cp)M12...p (Cp) + = A p p(Cp)A ∅ ∅ (Cp) + A p k (Cp) 2
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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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Page 277 and 278: The minimum is realized for S. Albe
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D. Bucur / Journal of Functional An
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lim n→∞ Ω lim sup n→∞
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