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Existence and nondegeneracy of ground states in critical free boundary problems

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Yang Yang, Kanishka Perera

Analysis of PDEs · Submitted 6 May 2014

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

The authors' main claim We extend the results of [30] to this problem by combining the method introduced there with the concentration compactness principle to overcome the difficulties arising from lack of compactness.

how it is stated · asserted 0.98 read the record →

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arXiv ID1405.1108 (version 3)
Pith ID5674HLLH, Pith's permanent record of this paper and its review
CitationKanishka Perera, Yang Yang. "Existence and nondegeneracy of ground states in critical free boundary problems." arXiv:1405.1108 (2014). https://pith.science/paper/5674HLLH
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,255 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.21 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. The corresponding study of higher critical points was recently initiated in Jerison and Perera [30, 31]. In particular, the existence and nondegeneracy of a mountain pass point in a superlinear and subcritical free boundary problem related to plasma confinement was proved in [30]. In this paper we study ground states of a critical free boundary problem related to the Brezis-Nirenberg problem [5]. We extend the results of [30] to this problem by combining the method introduced there with the concentration compactness principle to overcome the difficulties arising from lack of compactness.

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 Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. background 1.00 0.02 0.02 asserted 1.00
s1 The corresponding study of higher critical points was recently initiated in Jerison and Perera [30, 31]. background 0.98 0.03 0.02 asserted 1.00
s2 In particular, the existence and nondegeneracy of a mountain pass point in a superlinear and subcritical free boundary problem related to plasma confinement was proved in [30]. background 0.99 0.06 0.04 asserted 1.00
s3 In this paper we study ground states of a critical free boundary problem related to the Brezis-Nirenberg problem [5]. contribution 0.96 0.55 0.08 asserted 0.94
s4 We extend the results of [30] to this problem by combining the method introduced there with the concentration compactness principle to overcome the difficulties arising from lack of compactness. method 0.66 0.90 0.29 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • 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

Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. The corresponding study of higher critical points was recently initiated in Jerison and Perera [30, 31]. In particular, the existence and nondegeneracy of a mountain pass point in a superlinear and subcritical free boundary problem related to plasma confinement was proved in [30]. In this paper we study ground states of a critical free boundary problem related to the Brezis-Nirenberg problem [5]. We extend the results of [30] to this problem by combining the method introduced there with the concentration compactness principle to overcome the difficulties arising from lack of compactness.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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