Yet another proof of the density in energy of Lipschitz functions
Danka Lučić,
Enrico Pasqualetto
Abstract:We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the Newtonian–Sobolev space). Our result covers first-order Sobolev spaces of exponent $$p\in (1,\infty )$$
p
∈
(
1
,
∞
)
, defined over a complete separable metric s… Show more
We study first-order Sobolev spaces on reflexive Banach spaces via relaxation, test plans, and divergence. We show the equivalence of the different approaches to the Sobolev spaces and to the related tangent bundles.
We study first-order Sobolev spaces on reflexive Banach spaces via relaxation, test plans, and divergence. We show the equivalence of the different approaches to the Sobolev spaces and to the related tangent bundles.
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