Interpolation inequalities in pattern formation

Interpolation Inequalities in Pattern Formation

We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which wa...

Notes on Interpolation Inequalities

Relative rearrangement and interpolation inequalities

We prove here that the Poincaré-Sobolev pointwise inequalities for the relative rearrangement can be considered as the root of a great number of inequalities in various sets not necessarily vector spaces. In particular, new interpolation inequalities can be derived. Reordenamiento relativo y desigualdades de interpolación Resumen. Mostramos que las desigualdades puntuales de Poincaré-Sobolev pa...

Commutator Lifting Inequalities and Interpolation

In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foiaş, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative commutant lifting theorem. This is used to solve new operator-valued interpolation problems of SchurCarathéodory, Nevanlinna-Pick, and Sarason type on Fock s...

Mz Inequalities and Interpolation 3

We find necessary density conditions for Marcinkiewicz-Zygmund inequalities and interpolation for spaces of spherical harmonics in S with respect to the L norm. Moreover, we prove that there are no complete interpolation families for p 6= 2.