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An elliptic problem involving critical Choquard and singular discontinuous nonlinearity

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Gurdev C. Anthal, Jacques Giacomoni, Konijeti Sreenadh

Analysis of PDEs · Submitted 14 Sep 2023

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

The authors' main claim By applying variational methods and using the notion of generalized gradients for Lipschitz continuous functional, we obtain the existence and the multiplicity of weak solutions for some suitable range of $\lambda$ and $\gamma$.

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arXiv ID2309.07542 (version 1)
Pith IDGZSREKD7, Pith's permanent record of this paper and its review
CitationGurdev C. Anthal, Jacques Giacomoni, Konijeti Sreenadh. "An elliptic problem involving critical Choquard and singular discontinuous nonlinearity." arXiv:2309.07542 (2023). https://pith.science/paper/GZSREKD7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,037 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.04 · mentions code or data availability 0.01.

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

The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. By applying variational methods and using the notion of generalized gradients for Lipschitz continuous functional, we obtain the existence and the multiplicity of weak solutions for some suitable range of $\lambda$ and $\gamma$. Finally by studying the $L^\infty$-estimates and boundary behavior of weak solutions, we prove their H\"{o}lder and Sobolev regularity.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. contribution 0.94 0.85 0.18 asserted 0.89
s1 By applying variational methods and using the notion of generalized gradients for Lipschitz continuous functional, we obtain the existence and the multiplicity of weak solutions for some suitable range of $\lambda$ and $\gamma$. method 0.71 0.96 0.30 asserted 1.00
s2 Finally by studying the $L^\infty$-estimates and boundary behavior of weak solutions, we prove their H\"{o}lder and Sobolev regularity. result 0.83 0.95 0.32 asserted 1.00

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

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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

The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. By applying variational methods and using the notion of generalized gradients for Lipschitz continuous functional, we obtain the existence and the multiplicity of weak solutions for some suitable range of $\lambda$ and $\gamma$. Finally by studying the $L^\infty$-estimates and boundary behavior of weak solutions, we prove their H\"{o}lder and Sobolev regularity.

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