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Analytic regularity of a free boundary problem

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Huiqiang Jiang

Analysis of PDEs · Submitted 25 Oct 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most $n-8$.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0610770 (version 1)
Pith IDE2656DCD, Pith's permanent record of this paper and its review
CitationHuiqiang Jiang. "Analytic regularity of a free boundary problem." arXiv:math/0610770 (2006). https://pith.science/paper/E2656DCD
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,230 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.77 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.95 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most $n-8$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we consider a free boundary problem with volume constraint. background 0.82 0.58 0.03 asserted 0.64
s1 We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most $n-8$. result 0.99 0.95 0.94 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most $n-8$.

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