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Interpolation of operators

C. Bennett, +1 more
TLDR
In this article, the classical interpolation theorem is extended to the Banach Function Spaces, and the K-Method is used to find a Banach function space with a constant number of operators.
Abstract
Banach Function Spaces. Rearrangement-Invariant Banach Function Spaces. Interpolation of Operators on Rearrangement-Invariant Spaces. The Classical Interpolation Theorems. The K-Method. Each chapter includes references. Index.

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The Porous Medium Equation: Mathematical Theory

TL;DR: The Porous Medium Equation (PME) as discussed by the authors is one of the classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood.
Journal ArticleDOI

On ψ- interpolation spaces

TL;DR: In this article, the sequence Banach space ψ (Z) is defined for a class of convex functions ψ, and properties of the Kand Jinterpolation spaces (E0,E1)θ,ψ,K and (E 0,E 1) θ ∈ (0,1) are studied.
Journal ArticleDOI

Basic properties of strong mixing conditions. A survey and some open questions

TL;DR: In this paper, an update of, and a supplement to, a 1986 survey paper by the author on basic properties of strong mixing conditions is presented, which is an extension to the survey paper.
MonographDOI

The Porous Medium Equation

TL;DR: In this article, the authors introduced the notion of L1-limit solutions for the Dirichlet problem with nonhomogeneous data g 6 = 0 and showed that the L1 norm is a well-defined element of the L∞(Ω) space.
Journal ArticleDOI

A Theorem on Geometric Rigidity and the Derivation of Nonlinear Plate Theory from Three-Dimensional Elasticity

TL;DR: The energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by G. Kirchhoff in 1850 as mentioned in this paper, and it arises as a 0-limit of three-dimensional nonlinear elasticity theory as the thickness of a plate goes to zero.