INTERPOLATION INEQUALITIES IN W-1,W-p(S-1) AND CARRE DU CHAMP METHODS

Dolbeault J.; García-Huidobro M.; Manásevich R.

Abstract

This paper is devoted to an extension of rigidity results for nonlinear differential equations, based on carre 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 W-1,W-p(S-1) 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 carre 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 not equal 2.

Más información

Título según WOS: INTERPOLATION INEQUALITIES IN W-1,W-p(S-1) AND CARRE DU CHAMP METHODS
Título según SCOPUS: Interpolation inequalities in W1,p(S1) and Carré du champ methods
Título de la Revista: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volumen: 40
Número: 1
Editorial: AMER INST MATHEMATICAL SCIENCES-AIMS
Fecha de publicación: 2020
Página de inicio: 375
Página final: 394
Idioma: English
DOI:

10.3934/dcds.2020014

Notas: ISI, SCOPUS