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European Mathematical Society Publishing House
2024-03-28 12:00:58
5
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RLM&vol=25&iss=4&update_since=2024-03-28
Rendiconti Lincei - Matematica e Applicazioni
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.
RLM
1120-6330
1720-0768
General
10.4171/RLM
http://www.ems-ph.org/doi/10.4171/RLM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
25
2014
4
A fractional Gehring lemma, with applications to nonlocal equations
Tuomo
Kuusi
Aalto University, AALTO, FINLAND
Giuseppe
Mingione
Università di Parma, PARMA, ITALY
Yannick
Sire
Université Aix-Marseille, MARSEILLE CEDEX 13, FRANCE
Self-improving properties, non-local operators, elliptic equations
We describe a fractional version of the classical Gehring lemma. As a consequence, new self-improving regularity properties of solutions to integrodi¤erential equations emerge.
Partial differential equations
345
358
10.4171/RLM/683
http://www.ems-ph.org/doi/10.4171/RLM/683
The supercritical Lane–Emden equation and its gradient flow
Michael
Struwe
ETH Zürich, ZÜRICH, SWITZERLAND
Partial regularity, monotonicity formula, blow-up analysis
The following text is a summary of the author’s talk at the conference on "Nonlinear problems with singular data" at the Accademia dei Lincei, Rome, Novemver 26, 2013.
Partial differential equations
359
367
10.4171/RLM/684
http://www.ems-ph.org/doi/10.4171/RLM/684
Heat and mass transfer by convection in multicomponent Navier–Stokes mixtures: absence of subcritical instabilities and global nonlinear stability via the Auxiliary System Method
Salvatore
Rionero
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Convection, global stability, Auxiliary System Method
Because of its great geophysical relevance (engineering geology, volcanism, subsurface fluid motions,...) and the frequent applications (industrial processes, crystal growth, thermal engineering, air and water pollution,...) in the past as nowadays, the heat and mass transfer by convection in horizontal layers has attracted the attention of many scientists. In the present paper, this problem is investigated in the general case of a horizontal layer L - filled by a Navier-Stokes multicomponent fluid mixture - heated from below and salted (partly from below and partly from above) by $m\in\mathbb N$ salts $S_1,S_2,..., S_m$. Generalizing the Auxiliary System Method (AS Method), recently introduced for the Darcy fluid mixtures in porous layers \cite{33}-\cite{35}, it is shown that: i) for each Fourier component of the perturbation fields there exists an own nonlinear evolution system (auxiliary system); ii) via the auxiliary system, a linearization principle can be obtained; iii) the absence of subcritical instabilities and the property of the linear stability conditions to guarantee also the global nonlinear $L^2-$stability hold; iv) the Routh-Hurwitz stability conditions are characterized $\forall m\in\mathbb N$ and handled for $m\leq 2$; v) the looking for hidden symmetries and skew-symmetries allows to guarantee - via simple algebraic conditions in closed form - the global nonlinear stability.
Fluid mechanics
Partial differential equations
369
412
10.4171/RLM/685
http://www.ems-ph.org/doi/10.4171/RLM/685
Newton’s Philosophiae Naturalis Principia Mathematica "Jesuit" Edition: The Tenor of a Huge Work
Paolo
Bussotti
Alexander von Humboldt Stiftung, BERLIN, GERMANY
Raffaele
Pisano
Université Lille I, VILLENEUVE D'ASCQ CEDEX, FRANCE
Newton, Jesuit Edition, commentaries, relationships geometry-mathematics-physics, history of mathematics and physics
This paper has the aim to provide a general view of the so called Jesuit Edition (hereafter JE) of Newton’s Philosophiae Naturalis Principia Mathematica (1739–1742). This edition was conceived to explain all Newton’s methods through an apparatus of notes and commentaries. Every Newton’s proposition is annotated. Because of this, the text – in four volumes – is one of the most important documents to understand Newton’s way of reasoning. This edition is well known, but systematic works on it are still missing. We are going to fill this gap by means of a project exposed in the final remarks of this paper. In this paper we will: A) expound the way in which the notes and the additions to the JE were conceived by the commentators; B) provide some pieces of information about the commentators; C) summarize the most important of their notes; D) examine closely their notes as to a particularly important question: the so called "inverse problem of the central forces".
History and biography
413
444
10.4171/RLM/686
http://www.ems-ph.org/doi/10.4171/RLM/686
Estimates for $p$-Laplace type equation in a limiting case
Fernando
Farroni
Università Telematica Pegaso, NAPOLI, ITALY
Luigi
Greco
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Gioconda
Moscariello
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Dirichlet problem, $p$-Laplace operators, Orlicz–Sobolev spaces
We study the Dirichlet problem for a $p$-Laplacian type operator in the setting of the Orlicz–Zygmund space $\mathscr{L}^q\log^{-\alpha}\mathscr{L} \left(\Omega,\mathbb R^N\right)$, $q >1$ and $\alpha>0$. More precisely, our aim is to establish under which assuptions on $\alpha>0$ existence and uniqueness of the solution are assured.
Partial differential equations
445
448
10.4171/RLM/687
http://www.ems-ph.org/doi/10.4171/RLM/687