Pith. sign in

REVIEW 1 cited by

Trace and extension theorems for functions of bounded variation

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1511.04503 v2 pith:4OGWPBU7 submitted 2015-11-14 math.MG math.FA

Lukáš Malý , Nageswari Shanmugalingam , Marie Snipes This is my paper · ORCID
classification math.MGmath.FA
keywords omegapartialboundedtraceclassextensionfunctionfunctions
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

In this paper we show that every $L^1$-integrable function on $\partial\Omega$ can be obtained as the trace of a function of bounded variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary $\partial\Omega$ in a doubling metric measure space. In particular, the trace class of $BV(\Omega)$ is $L^1(\partial\Omega)$ provided that $\Omega$ supports a 1-Poincar\'e inequality. We also construct a bounded linear extension from a Besov class of functions on $\partial\Omega$ to $BV(\Omega)$.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Prediction error certification for PINNs: Theory, computation, and application to Stokes flow

    math.NA 2025-08 conditional novelty 6.0 of 10

    A modified semigroup-based error bound makes PINN error certification applicable to Stokes flow, but the practical certification is not fully rigorous.

Pith tools