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Existence results for a nonlinear nonautonomus transmission problem via domain perturbation

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Matteo Dalla Riva, Riccardo Molinarolo, Paolo Musolino

Analysis of PDEs · Submitted 23 Nov 2022

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

The authors' main claim In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation.

how it is stated · asserted 0.90 read the record →

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arXiv ID2211.13105 (version 1)
Pith ID7PT46LON, Pith's permanent record of this paper and its review
CitationMatteo Dalla Riva, Paolo Musolino, Riccardo Molinarolo. "Existence results for a nonlinear nonautonomus transmission problem via domain perturbation." arXiv:2211.13105 (2022). https://pith.science/paper/7PT46LON
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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, 3,573 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$.

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 study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. contribution 0.99 0.86 0.22 asserted 0.90
s1 The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. background 0.55 0.42 0.03 asserted 1.00
s2 First we analyse the case in which the inclusion is a fixed domain. method 0.88 0.82 0.03 asserted 0.82
s3 Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$. contribution 0.69 0.83 0.18 asserted 0.93

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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  • C citations
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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

The paper
Original abstract

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$.

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