Quantum mechanics

Context (archaeology)

Pure mathematics

Biology

Equivalence (formal languages)

Operating system

Computer science

Geology

Universality (dynamical systems)

Lipschitz continuity

Paleontology

Physics

Database

Upper and lower bounds

Mathematics

Mathematical analysis

Geometry

Measure (data warehouse)

Sobolev space

Radon measure

Euclidean space

Euclidean geometry

Space (punctuation)

Locally compact space

Annali di Matematica Pura ed Applicata (1923 -)

In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz functions.

Characterisation of upper gradients on the weighted Euclidean space and applications