A global compactness theorem for critical p-Laplace equations with weights
Bibliographic record
Abstract
Let n ≥ 2, fix 1 < p < n, and let Ω ⊂ R n be a bounded domain, with possibly non-smooth boundary, containing the origin.We investigate the compactness of Palais-Smale sequences for a class of critical p-Laplace equations with weights.More precisely, we establish a Struwe-type decomposition result for Palais-Smale sequences extending the recent result of to weighted equations.In sharp contrast to the model case of the critical p-Laplace equation, all bubbling must occur at the origin.Furthermore, we do not impose any smoothness assumptions on the boundary of Ω and our Palais-Smale sequence may be sign-changing.En tout premier lieu, je voudrais remercier mon superviseur, le professeur Jérôme Vétois, pour ses conseils, ses encouragements inébranlables et son appui indéfectible.Sans son soutien et les heures incalculables qu'il a consacré à répondre à mes nombreuses questions, cette thèse n'aurait pas été possible.Je voudrais aussi exprimer ma gratitude envers mon co-superviseur le professeur Pengfei Guan pour ses commentaires constructifs et tout le temps qu'il a investi dans ce travail.Je souhaiterais également remercier le professeur Guan, le professeur Vétois et le département de mathématiques et de statistique pour leur soutien financier.De plus, je suis très reconnaissant envers les nombreux professeurs et étudiants dont le travail acharné m'a encouragé à me surpasser.Surtout, je tiens à remercier Dana Berman pour des discussions utiles et ses suggestions pour l'organisation de ce travail.Enfin, je veux remercier mes parents pour leur amour et leur soutien infini.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".