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2018•ITM Web of ConferencesOpen access

Optimal Lipschitz extensions

Thanh Viet Phan

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Abstract

The classical Lipschitz extension problem in concerned for conditions on a pair of metric spaces(X,dX)and(Y,dY)such that for all Ω ⊂ X and for all Lipschitz function and for all Lipschitz functionf : Ω → Y, then there is a functiong : X → Ythat extendsfand has the same Lipschitz constant asf. In this paper we discuss some results and open questions related to that issue.

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The classical Lipschitz extension problem in concerned for conditions on a pair of metric spaces(X,dX)and(Y,dY)such that for all Ω ⊂ X and for all Lipschitz function and for all Lipschitz functionf : Ω → Y, then there is a functiong : X → Ythat extendsfand has the same Lipschitz constant asf. In this paper we discuss some results and open questions related to that issue.

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Available abstract

The classical Lipschitz extension problem in concerned for conditions on a pair of metric spaces(X,dX)and(Y,dY)such that for all Ω ⊂ X and for all Lipschitz function and for all Lipschitz functionf : Ω → Y, then there is a functiong : X → Ythat extendsfand has the same Lipschitz constant asf. In this paper we discuss some results and open questions related to that issue.

Key concepts: Lipschitz continuity, Lipschitz domain, Metric map, Extension (predicate logic), Mathematics, Function (biology), Pure mathematics, Metric (unit)

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