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Compactness methods for $\Gamma^{1,\alpha}$ boundary Schauder estimates in Carnot groups

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Agnid Banerjee, Nicola Garofalo, Isidro Munive

Analysis of PDEs · Submitted 18 Apr 2018

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

The authors' main claim The aim of this paper is to prove $\Gamma^{1,\alpha}$ Schauder estimates near a $C^{1,\alpha}$ non-characteristic portion of the boundary for $\Gamma^{0, \alpha}$ perturbations of horizontal Laplaceans in Carnot groups.

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arXiv ID1804.06697 (version 2)
Pith IDZPTJI36O, Pith's permanent record of this paper and its review
CitationAgnid Banerjee, Isidro Munive, Nicola Garofalo. "Compactness methods for $\Gamma^{1,\alpha}$ boundary Schauder estimates in Carnot groups." arXiv:1804.06697 (2018). https://pith.science/paper/ZPTJI36O
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,354 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.25 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.07 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; .

The aim of this paper is to prove $\Gamma^{1,\alpha}$ Schauder estimates near a $C^{1,\alpha}$ non-characteristic portion of the boundary for $\Gamma^{0, \alpha}$ perturbations of horizontal Laplaceans in Carnot groups. This situation of minimally smooth domains presents itself naturally in the study of subelliptic free boundary problems of obstacle type, see [15].

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 The aim of this paper is to prove $\Gamma^{1,\alpha}$ Schauder estimates near a $C^{1,\alpha}$ non-characteristic portion of the boundary for $\Gamma^{0, \alpha}$ perturbations of horizontal Laplaceans in Carnot groups. contribution 0.98 0.68 0.51 asserted 0.99
s1 This situation of minimally smooth domains presents itself naturally in the study of subelliptic free boundary problems of obstacle type, see [15]. background 0.89 0.05 0.03 asserted 0.99

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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

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Original abstract

The aim of this paper is to prove $\Gamma^{1,\alpha}$ Schauder estimates near a $C^{1,\alpha}$ non-characteristic portion of the boundary for $\Gamma^{0, \alpha}$ perturbations of horizontal Laplaceans in Carnot groups. This situation of minimally smooth domains presents itself naturally in the study of subelliptic free boundary problems of obstacle type, see [15].

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  • In a free boundary problem one does not a priori know the higher regularity of the free boundary, and consequently the results in [ref] cannot be applied in such situations; 2) in [ref] the authors work with non-divergence form equations and $Γ^α$ coefficients.

    Schauder estimates at the boundary for sub-laplacians in Carnot groups · Introduction · 0.88

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