Real-valued valuations on Sobolev spaces

Abstract

Continuous, SL($n$) and translation invariant real-valued valuations on Sobolev spaces are classified.

21 pages

References in corpus (2)

• Monotone valuations on the space of convex functions
• $L_p$-Blaschke Valuations

Cited by in corpus (10)

• Valuations on Convex Functions
• Minkowski valuations on convex functions
• A homogeneous decomposition theorem for valuations on convex functions
• Laplace transforms and valuations
• The support of dually epi-translation invariant valuations on convex functions
• Volume, Polar Volume and Euler Characteristic for Convex Functions
• $\mathrm{SL}(n)$ invariant valuations on super-coercive convex functions
• Valuations on Log-Concave Functions
• Valuations on Convex Bodies and Functions
• The Legendre transform, the Laplace transform and valuations