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pro vyhledávání: '"Dupaigne"'
We consider the Lane-Emden system-$\Delta$u = |v| p-1 v,-$\Delta$v = |u| q-1 u in R d. When p $\ge$ q $\ge$ 1, it is known that there exists a positive radial stable solution (u, v) $\in$ C 2 (R d) if and only if d $\ge$ 11 and (p, q) lies on or abov
Externí odkaz:
http://arxiv.org/abs/2312.07097
Autor:
Akbar Zainu, Pauline Dupaigne, Soumya Bouchouika, Julien Cau, Julie A. J. Clément, Pauline Auffret, Virginie Ropars, Jean-Baptiste Charbonnier, Bernard de Massy, Raphael Mercier, Rajeev Kumar, Frédéric Baudat
Publikováno v:
Nature Communications, Vol 15, Iss 1, Pp 1-20 (2024)
Abstract During meiosis, nucleoprotein filaments of the strand exchange proteins RAD51 and DMC1 are crucial for repairing SPO11-generated DNA double-strand breaks (DSBs) by homologous recombination (HR). A balanced activity of positive and negative R
Externí odkaz:
https://doaj.org/article/b23ba1e45f564ac9871d10aea2621def
We prove that 0 the only classical solution of the Lane-Emden equation in the half-space which is stable outside a compact set. We also consider weak solutions and the case of general cones.
Externí odkaz:
http://arxiv.org/abs/2207.06049
We are interested in the Caffarelli-Kohn-Nirenberg inequality (CKN in short), introduced by these authors in 1984. We explain why the CKN inequality can be viewed as a Sobolev inequality on a weighted Riemannian manifold. More precisely, we prove tha
Externí odkaz:
http://arxiv.org/abs/2111.15383
Autor:
Dupaigne, Louis, Farina, Alberto
In the present paper, we investigate the regularity and symmetry properties of weak solutions to semilinear elliptic equations which are locally stable.
Externí odkaz:
http://arxiv.org/abs/2102.12157
In this note we present a new proof of Sobolev's inequality under a uniform lower bound of the Ricci curvature. This result was initially obtained in 1983 by Ilias. Our goal is to present a very short proof, to give a review of the famous inequality
Externí odkaz:
http://arxiv.org/abs/2011.07840
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on fini
Externí odkaz:
http://arxiv.org/abs/2003.11466
Autor:
Dupaigne, Louis, Farina, ALberto
Publikováno v:
Analysis & PDE 15 (2022) 551-566
We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.
Externí odkaz:
http://arxiv.org/abs/1912.11639
Publikováno v:
In Journal of Functional Analysis 15 May 2023 284(10)