lipschitz vector field:decomposition of l2

decomposition of l2

decomposition of l2

Herebyavectorfieldisexpressedasthesumoftwoharmonicgradients(one...thesequestionsforLipschitzsurfacesandvectorfieldsofL2-class.This ...。其他文章還包含有:「DeterminingLipschitzconstantforaspecialvectorfield」、「Existenceanduniquenessforthetransportofcurrentsby...」、「Lipschitzcontinuity」、「Poincaré」、「realanalysis」、「Theflowboxtheoremfordivergence」、「Vector」、「[1606.05486]OnLipschi...

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Determining Lipschitz constant for a special vector field
Determining Lipschitz constant for a special vector field

https://math.stackexchange.com

I want to determine a good Lipschitz constant for this vector field, i.e. find L such that for all x,y∈C we have ‖v(x)−v(y)‖≤L‖x−y‖.

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Existence and uniqueness for the transport of currents by ...
Existence and uniqueness for the transport of currents by ...

https://arxiv.org

Existence and uniqueness for the transport of currents by Lipschitz vector fields. Authors:Paolo Bonicatto, Giacomo Del Nin, Filip Rindler.

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Lipschitz continuity
Lipschitz continuity

https://en.wikipedia.org

In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions.

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Poincaré
Poincaré

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1. Introduction and statement of the result. The Poincaré inequality is one of the main tools in the proof of regularity of solutions of PDEs in divergence ...

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real analysis
real analysis

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My problem is i don't know how Lipschitz continuity works for vector functions. I am planning to show lipschitz continuity component-wise.

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The flowbox theorem for divergence
The flowbox theorem for divergence

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We say that a Lipschitz vector field X is divergence-free if ∇ ⋅ X = 0 for ν-a.e. x ∈ M . We denote this set by X ν 0 , 1 ( M ) .

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Vector
Vector

https://www.bodysoulmath.org

We now turn to the extension of the basic concepts of real-valued functions of one real variable, such as Lipschitz continuity and differentiability, to vector- ...

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[1606.05486] On Lipschitz vector fields and the Cauchy ...
[1606.05486] On Lipschitz vector fields and the Cauchy ...

https://arxiv.org

Abstract:We introduce a class of Lipschitz horizontal vector fields in homogeneous groups, for which we show equivalent descriptions, ...