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The fractional porous medium equation on noncompact Riemannian manifolds

Publicated to:MATHEMATISCHE ANNALEN. 389 (4): 1-49 - 2024-01-01 389(4), DOI: 10.1007/s00208-023-02731-6

Authors: Berchio, E.; Bonforte, M.; Grillo, G.; Muratori, M.

Affiliations

Politecn Milan, Dipartimento Matemat, Piazza Leonardo Vinci 32, I-20133 Milan, Italy - Author
Politecn Torino, Dipartimento Sci Matematiche, Corso Duca Abruzzi 24, I-10129 Turin, Italy - Author
Politecnico di Milano - Author
Politecnico di Torino - Author
UCM, Inst Ciencias Matemat ICMAT, UAM UC3M, CSIC, Campus Cantoblanco, Madrid 28049, Spain - Author
Univ Autonoma Madrid, Dept Matemat, Campus Cantoblanco, Madrid 28049, Spain - Author
Universidad Autónoma de Madrid - Author
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Abstract

We study nonnegative solutions to the fractional porous medium equation on a suitable class of connected, noncompact Riemannian manifolds. We provide existence and smoothing estimates for solutions, in an appropriate weak (dual) sense, for data belonging either to the usual L1 space or to a considerably larger weighted space determined in terms of the fractional Green function. The class of manifolds for which the results hold includes both the Euclidean and the hyperbolic spaces and even in the Euclidean situation involves a class of data which is larger than the previously known one.

Keywords

asymptotic-behaviorexistencekernellaplacianregularityuniquenessDegenerate diffusion-equations

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal MATHEMATISCHE ANNALEN due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 67/490, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 3.51, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-27, the following number of citations:

  • Scopus: 3

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-27:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 2 (PlumX).

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Italy.