
Interpolation inequalities in W1,p(S1) and carré du champ methods
Dolbeault, Jean; Garcia-Huidobro, Marta; Manásevich, Raul (2020), Interpolation inequalities in W1,p(S1) and carré du champ methods, Discrete and Continuous Dynamical Systems. Series A, 40, 1, p. 375-394. 10.3934/dcds.2020014
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Type
Article accepté pour publication ou publiéDate
2020Journal name
Discrete and Continuous Dynamical Systems. Series AVolume
40Number
1Publisher
AIMS - American Institute of Mathematical Sciences
Pages
375-394
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Show full item recordAuthor(s)
Dolbeault, Jean
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Garcia-Huidobro, Marta
Manásevich, Raul
Centre de Modélisation Mathématique / Centro de Modelamiento Matemático [CMM]
Departamento de Ingeniería Matemática [Santiago] [DIM]
Abstract (EN)
This paper is devoted to an extension of rigidity results for nonlinear differential equations, based on carré du champ methods, in the one-dimensional periodic case. The main result is an interpolation inequality with non-trivial explicit estimates of the constants in W1,p(S1) with p ≥ 2. Mostly for numerical reasons, we relate our estimates with issues concerning periodic dynamical systems. Our interpolation inequalities have a dual formulation in terms of generalized spectral estimates of Keller-Lieb-Thirring type, where the differential operator is now a p-Laplacian type operator. It is remarkable that the carré du champ method adapts to such a nonlinear framework, but significant changes have to be done and, for instance, the underlying parabolic equation has a nonlocal term whenever p≠2.Subjects / Keywords
rescaling; period; nonlinear Keller-Lieb-Thirring energy estimates; bifurcation; carré du champ method; p-Laplacian; Fisher information; entropy; elliptic equations; Interpolation; Gagliardo-Nirenberg inequalities; rigidity; Poincaré inequality; uniqueness; branches of solutionsRelated items
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Dolbeault, Jean; Garcia-Huidobro, Marta; Manásevich, Raul (2019) Document de travail / Working paper
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Manásevich, Raul; Garcia-Huidobro, Marta; Dolbeault, Jean (2013) Article accepté pour publication ou publié
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Dolbeault, Jean; Garcia-Huidobro, Marta; Manásevich, Raul (2023) Document de travail / Working paper
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Manásevich, Raul; Garcia-Huidobro, Marta; Dolbeault, Jean; Cortázar, Carmen (2014) Article accepté pour publication ou publié
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