Pervasiveness of the p-Laplace operator under localization of fractional g-Laplace operators
Bibliographic record
Abstract
In this paper, we analyze the behavior of the truncated functionals aswhere G is an Orlicz function which is assumed to be regularly varying at 0. A prototype of such function is given by G(t) = t p (1+| log(t)|) with p ≥ 2. These kinds of functionals arise naturally in peridynamics, where long-range interactions are neglected and only those that exerted at distance smaller than δ > 0 are taken into account, i.e., the horizon δ > 0 represents the range of interactions or nonlocality.This paper is inspired by the celebrated result by Bourgain, Brezis and Mironescu, who analyzed the limit s → 1 -with G(t) = t p .In particular, we prove that, under appropriate conditions,and an explicit constant K N,p > 0.Moreover, the converse is also true if the above localization limit exist as δ → 0 + , and the Orlicz function G is a regularly varying function with index(G) = p.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".