Sobolev Spaces in Extended Metric-Measure Spaces

Savaré, Giuseppe

doi:10.1007/978-3-030-84141-6_4

Cited by 7 publications

(1 citation statement)

References 42 publications

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“…Overall, the research paper contributes to our understanding of Sobolev spaces and their implications for function behavior on compact manifolds, with applications in various mathematical and scientific fields. More literature can be obtained from [1,2,3,4,5]…”

Section: Introductionmentioning

confidence: 99%

Interplay of Sobolev Spaces on Compact Manifolds: Embedding Theorems, Inequalities, and Compactness

Evans,

Apima

2024

AIR

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This research paper explores various properties of Sobolev spaces on compact manifolds, focusing on embedding theorems, compactness, and inequalities. We establish the compact embedding of Sobolev spaces into continuous and Lebesgue spaces, as well as the continuity and compactness of embeddings between different Sobolev spaces. We also derive inequalities involving the Laplacian and gradients of functions, providing insights into their behavior on manifolds. These results contribute to our understanding of the interplay between function smoothness, continuity, and distribution on compact manifolds.

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Section: Introductionmentioning

confidence: 99%

Interplay of Sobolev Spaces on Compact Manifolds: Embedding Theorems, Inequalities, and Compactness

Evans,

Apima

2024

AIR

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Vector calculus on weighted reflexive Banach spaces

Pasqualetto,

Rajala

2024

Math. Z.

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Yet another proof of the density in energy of Lipschitz functions

Lučić,

Pasqualetto

2024

manuscripta math.

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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 space endowed with a boundedly-finite Borel measure. Our proof is based on a completely smooth analysis: first we reduce the problem to the Banach space setting, where we consider smooth functions instead of Lipschitz ones, then we rely on classical tools in convex analysis and on the superposition principle for normal 1-currents. Along the way, we obtain a new proof of the density in energy of smooth cylindrical functions in Sobolev spaces defined over a separable Banach space endowed with a finite Borel measure.

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Sobolev Spaces in Extended Metric-Measure Spaces

Cited by 7 publications

References 42 publications

Interplay of Sobolev Spaces on Compact Manifolds: Embedding Theorems, Inequalities, and Compactness

Interplay of Sobolev Spaces on Compact Manifolds: Embedding Theorems, Inequalities, and Compactness

Vector calculus on weighted reflexive Banach spaces

Yet another proof of the density in energy of Lipschitz functions

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