Movatterモバイル変換

[0]ホーム
URL:

×

zbMATH Open — the first resource for mathematics

from until
Reset all

Examples

GeometrySearch for the termGeometry inany field. Queries arecase-independent.
Funct*Wildcard queries are specified by* (e .g.functions,functorial, etc.). Otherwise the search isexact.''Topological group'':Phrases (multi - words) should be set in''straight quotation marks''.
au: Bourbaki & ti: AlgebraSearch forauthorBourbaki andtitleAlgebra. Theand-operator & is default and can be omitted.
Chebyshev | TschebyscheffTheor-operator| allows to search forChebyshev orTschebyscheff.
Quasi* map* py: 1989The resulting documents havepublicationyear1989.
so:Eur* J* Mat* Soc* cc:14Search for publications in a particularsource with aMathematics SubjectClassificationcode in14.
cc:*35 ! any:ellipticSearch for documents about PDEs (prefix with * to search only primary MSC); the not-operator ! eliminates all results containing the wordelliptic.
dt: b & au: HilbertThedocumenttype is set tobooks; alternatively:j forjournal articles,a forbookarticles.
py: 2000 - 2015 cc:(94A | 11T)Numberranges when searching forpublicationyear are accepted . Terms can be grouped within( parentheses).
la: chineseFind documents in a givenlanguage .ISO 639 - 1 (opens in new tab) language codes can also be used.
st: c r sFind documents that arecited, havereferences and are from asingle author.

Fields

ab Text from the summary or review (for phrases use “. ..”)
an zbMATH ID, i.e.: preliminary ID, Zbl number, JFM number, ERAM number
any Includes ab, au, cc, en, rv, so, ti, ut
arxiv arXiv preprint number
au Name(s) of the contributor(s)
br Name of a person with biographic references (to find documents about the life or work)
cc Code from the Mathematics Subject Classification (prefix with* to search only primary MSC)
ci zbMATH ID of a document cited in summary or review
db Database: documents in Zentralblatt für Mathematik/zbMATH Open (db:Zbl), Jahrbuch über die Fortschritte der Mathematik (db:JFM), Crelle's Journal (db:eram), arXiv (db:arxiv)
dt Type of the document: journal article (dt:j), collection article (dt:a), book (dt:b)
doi Digital Object Identifier (DOI)
ed Name of the editor of a book or special issue
en External document ID: DOI, arXiv ID, ISBN, and others
in zbMATH ID of the corresponding issue
la Language (use name, e.g.,la:French, orISO 639-1, e.g.,la:FR)
li External link (URL)
na Number of authors of the document in question. Interval search with “-”
pt Reviewing state: Reviewed (pt:r), Title Only (pt:t), Pending (pt:p), Scanned Review (pt:s)
pu Name of the publisher
py Year of publication. Interval search with “-”
rft Text from the references of a document (for phrases use “...”)
rn Reviewer ID
rv Name or ID of the reviewer
se Serial ID
si swMATH ID of software referred to in a document
so Bibliographical source, e.g., serial title, volume/issue number, page range, year of publication, ISBN, etc.
st State: is cited (st:c), has references (st:r), has single author (st:s)
sw Name of software referred to in a document
ti Title of the document
ut Keywords

Operators

a & bLogical and (default)
a | bLogical or
!abLogical not
abc*Right wildcard
ab cPhrase
(ab c)Term grouping

See also ourGeneral Help.

Improved interpolation inequalities and stability.(English)Zbl 1437.26018

Summary: For exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere withcarré du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates of the optimal constants in the symmetry breaking range and stability estimates for the optimal functions. Some of these results can be reformulated in the Euclidean space using the stereographic projection.

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
58E35 Variational inequalities (global problems) in infinite-dimensional spaces

Cite

References:

[1]A. Arnold and J. Dolbeault, Refined convex Sobolev inequalities, J. Funct. Anal. 225 (2005), no. 2, 337-351. ·Zbl 1087.35018
[2]D. Bakry and M. Émery, Diffusions hypercontractives, Séminaire de Probabilités. XIX. 1983/84, Lecture Notes in Math. 1123, Springer, Berlin (1985), 177-206. ·Zbl 0561.60080
[3]D. Bakry and M. Émery, Inégalités de Sobolev pour un semi-groupe symétrique, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 8, 411-413. ·Zbl 0579.60079
[4]D. Bakry, I. Gentil and M. Ledoux, Analysis and Geometry of Markov Diffusion Operators, Grundlehren Math. Wiss. 348, Springer, Cham, 2014. ·Zbl 1376.60002
[5]W. Beckner, Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Ann. of Math. (2) 138 (1993), no. 1, 213-242. ·Zbl 0826.58042
[6]G. Bianchi and H. Egnell, A note on the Sobolev inequality, J. Funct. Anal. 100 (1991), no. 1, 18-24. ·Zbl 0755.46014
[7]M.-F. Bidaut-Véron and L. Véron, Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations, Invent. Math. 106 (1991), no. 3, 489-539. ·Zbl 0755.35036
[8]M. J. Cáceres, J. A. Carrillo and J. Dolbeault, Nonlinear stability in L^p for a confined system of charged particles, SIAM J. Math. Anal. 34 (2002), no. 2, 478-494. ·Zbl 1015.35015
[9]J. Demange, Improved Gagliardo-Nirenberg-Sobolev inequalities on manifolds with positive curvature, J. Funct. Anal. 254 (2008), no. 3, 593-611. ·Zbl 1133.58012
[10]J. Dolbeault, M. J. Esteban, M. Kowalczyk and M. Loss, Sharp interpolation inequalities on the sphere: new methods and consequences, Chin. Ann. Math. Ser. B 34 (2013), no. 1, 99-112. ·Zbl 1263.26029
[11]J. Dolbeault, M. J. Esteban, M. Kowalczyk and M. Loss, Improved interpolation inequalities on the sphere, Discrete Contin. Dyn. Syst. Ser. S 7 (2014), no. 4, 695-724. ·Zbl 1290.26022
[12]J. Dolbeault, M. J. Esteban and A. Laptev, Spectral estimates on the sphere, Anal. PDE 7 (2014), 435-460. ·Zbl 1293.35183
[13]J. Dolbeault, M. J. Esteban, A. Laptev and M. Loss, Spectral properties of Schrödinger operators on compact manifolds: Rigidity, flows, interpolation and spectral estimates, C. R. Math. Acad. Sci. Paris 351 (2013), no. 11-12, 437-440. ·Zbl 1276.58007
[14]J. Dolbeault, M. J. Esteban and M. Loss, Nonlinear flows and rigidity results on compact manifolds, J. Funct. Anal. 267 (2014), no. 5, 1338-1363. ·Zbl 1294.58005
[15]J. Dolbeault, M. J. Esteban and M. Loss, Interpolation inequalities, nonlinear flows, boundary terms, optimality and linearization, J. Elliptic Parabol. Equ. 2 (2016), no. 1-2, 267-295. ·Zbl 1386.35174
[16]J. Dolbeault, M. J. Esteban and M. Loss, Interpolation inequalities on the sphere: Linear vs. nonlinear flows, Ann. Fac. Sci. Toulouse Math. (6) 26 (2017), no. 2, 351-379. ·Zbl 1372.58017
[17]J. Dolbeault, M. J. Esteban, M. Loss and M. Muratori, Symmetry for extremal functions in subcritical Caffarelli-Kohn-Nirenberg inequalities, C. R. Math. Acad. Sci. Paris 355 (2017), no. 2, 133-154. ·Zbl 1379.49009
[18]J. Dolbeault and X. Li, φ-entropies: Convexity, coercivity and hypocoercivity for Fokker-Planck and kinetic Fokker-Planck equations, Math. Models Methods Appl. Sci. 28 (2018), no. 13, 2637-2666. ·Zbl 1411.82032
[19]J. Dolbeault and G. Toscani, Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities, Int. Math. Res. Not. IMRN 2016 (2016), no. 2, 473-498. ·Zbl 1355.46038
[20]C. E. Mueller and F. B. Weissler, Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere, J. Funct. Anal. 48 (1982), no. 2, 252-283. ·Zbl 0506.46022
[21]A. Unterreiter, A. Arnold, P. Markowich and G. Toscani, On generalized Csiszár-Kullback inequalities, Monatsh. Math. 131 (2000), no. 3, 235-253. ·Zbl 1015.94003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
© 2025FIZ Karlsruhe GmbHPrivacy PolicyLegal NoticesTerms & Conditions
  • Mastodon logo
 (opens in new tab)
[8]ページ先頭
©2009-2025 Movatter.jp