Fetching the paper…
Reading the bibliography…
Starting from the quantitative stability result of Bianchi and Egnell for the 2-Sobolev inequality, we deduce several different stability results for a Gagliardo-Nirenberg-Sobolev inequality in the plane.
Rosen, G (1971) Minimum value for c c in the Sobolev inequality ‖ ϕ 3 ‖ ≤ c ‖ ∇ ϕ ‖ 3 {\|}{\phi^{3}}{\|}\leq c{\|}{\nabla\phi}{\|}^{3} . SIAM J. Appl. Math. 21 (1971), 30-32
1971
Earlier work this paper cites.
Aubin, Th (1976) Problémes isoperimétriques et espaces de Sobolev. J. Differ. Geometry 11, 573-598
1976
Earlier work this paper cites.
Talenti G, (1976) Best constants in Sobolev inequality. Ann. Mat. Pura Appl. 110 , 353-372
1976
Earlier work this paper cites.
Lieb EH, (1983) Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math., 118: 349–374
1983
Earlier work this paper cites.
Herrero MA, Pierre M (1985) The Cauchy problem for u t = Δ u m u_{t}=\Delta u^{m} when 0 < m < 1 0<m<1 , Trans. AMS, 291: 145–158
1985
Earlier work this paper cites.
Bianchi G, Egnell H (1991) A note on the Sobolev inequality, J. Funct. Anal., 100: 18–24
1991
Earlier work this paper cites.
Carlen EA, Loss M (1992) Competing symmetries, the logarithmic HLS inequality and Onofri’s inequality on S n S^{n} , Geom. Funct. Anal., 2: 90–104
1992
Earlier work this paper cites.
Beckner W (1993) Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Ann. of Math. 2, 138: 213–242
1993
Earlier work this paper cites.
Carlen EA, Loss M. (1993) Sharp constant in NashÕs inequality. Internat. Math. Res. Notices, 7 :213-215
1993
Earlier work this paper cites.
Lieb EH, Loss M, (1997) Analysis. Graduate Studies in Mathematics, 14. American Mathematical Society, Providence, RI,
1997
Cited alongside, same era.
McCann RJ, (1997) A convexity principle for interacting gases, Adv. Math. 128: 153–179
1997
Cited alongside, same era.
Otto F (2001) The geometry of dissipative evolution equations: the porous medium equation, Comm. Partial Differential Equations, 26: 101–174
2001
Cited alongside, same era.
Del Pino M, Dolbeault J (2002) Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions, Jour. Math. Pures Appl., 81: 301–342
2002
Cited alongside, same era.
Carrillo JA, Vázquez JL (2003) Fine asymptotics for fast diffusion equations, Comm. Partial Differential Equations, 28: 1023–1056
2003
Cited alongside, same era.
Bonforte M, Vázquez JL (2006) Global positivity estimates and Harnack inequalities for the fast diffusion equation, Jour. Func. Analysis, 240: 399–428
2006
Later among the works it cites.
Fusco N, Maggi F, Pratelli A (2007) The sharp quantitative Sobolev inequality for functions of bounded variation. J. Func. Anal., 244: 315–341
2007
Later among the works it cites.
Vázquez JL (2007) The Porous Medium Equation. Mathematical theory, Oxford Mathematical Monographs, The Clarendon Press/Oxford University Press, Oxford/New York
2007
Later among the works it cites.
Fusco N, Maggi F, Pratelli A (2008) The sharp quantitative isoperimetric inequality. Ann. of Math., 168: 941–980
2008
Later among the works it cites.
Blanchet A, Bonforte M, Dolbeault J, Grillo G, Vázquez JL (2009) Asymptotic of the fast diffusion equation via entropy estimates, Arch. Rational. Mech. Anal., 191: 347–385
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Vázquez JL (2003) Asymptotic behaviour for the porous medium equation posed in the whole space, J. Evol. Equ., 3: 67–118
2003
Cited alongside, same era.
Cordero -Erausqauin D, Nazaret B, Villani C (2004) A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities, Adv. Math. 182, no. 2, 307-332
2004
Cited alongside, same era.
Dolbeault J, Perthame B, (2004) Optimal critical mass in the two-dimensional Keller- Segel model in ℝ 2 {\mathord{\mathbb{R}}}^{2} , C. R. Math. Acad. Sci. Paris, 339 , pp. 611-616
2004
Cited alongside, same era.
Ambrosio L, Gigli N, Savaré G (2005) Gradient flows in metric spaces and in the space of probability measures. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel
2005
Cited alongside, same era.
Barky D, Gentil Y, Ledoux M, Analysis and geometry of diffusion semigroups. Monograph in preparation
Cited in the paper.
Figalli A, Maggi F, Pratelli A, Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation. Preprint
Cited in the paper.
2009
Later among the works it cites.
Cianchi A, Fusco N, Maggi F, Pratelli A (2009) The sharp Sobolev inequality in quantitative form. J. Eur. Math. Soc. (JEMS) 11: 1105–1139
2009
Later among the works it cites.
Blanchet A, Carlen EA, Carrillo JA (2010) Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model, to appear in Jour. Func. Analysis
2010
Later among the works it cites.
Carlen EA, Carrilo JA, Loss M (2010) Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows, P.N.A.S. 107 (46) 19696–19701
2010
Later among the works it cites.
Figalli A, Maggi F, Pratelli A (2010) A mass transportation approach to quantitative isoperimetric inequalities. Inventiones Mathematicae, 182: 167–211
2010
Later among the works it cites.