Displaying similar documents to “On Mazurkiewicz sets”

A two well Liouville theorem

Andrew Lorent (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we analyse the structure of approximate solutions to the compatible two well problem with the constraint that the surface energy of the solution is less than some fixed constant. We prove a quantitative estimate that can be seen as a two well analogue of the Liouville theorem of Friesecke James Müller. Let H = σ 0 0 σ - 1 for σ > 0 . Let 0 < ζ 1 < 1 < ζ 2 < ∞ . Let K : = S O 2 ∪ S O 2 H . Let u ∈ W 2 , 1 Q 1 0 be a C 1 invertible bilipschitz function with Lip u < ζ 2 , Lip u - 1 < ζ 1 - 1 . There exists positive constants 𝔠 1 < 1 and 𝔠 2 > 1 depending only on σ , ζ 1 , ζ 2 such that if ϵ ∈ 0 , 𝔠 1 and u ...

On the selector of twin functions

Marian Turzański (1998)

Commentationes Mathematicae Universitatis Carolinae

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A theorem is proved which could be considered as a bridge between the combinatorics which have a beginning in the dyadic spaces theory and the partition calculus.