-
1
-
-
0013528564
-
General logarithmic Sobolev inequalities and Orlicz embedding
-
Adams R. A.: General logarithmic Sobolev inequalities and Orlicz embedding. J. Funct. Anal. 34, 292-303 (1979).
-
(1979)
J. Funct. Anal.
, vol.34
, pp. 292-303
-
-
Adams, R.A.1
-
2
-
-
84972498579
-
Problèmes isopérimétriques etespaces de Sobolev
-
Aubin T.: Problèmes isopérimétriques et espaces de Sobolev. J. Differ. Geom. 11, 573-598 (1976).
-
(1976)
J. Differ. Geom.
, vol.11
, pp. 573-598
-
-
Aubin, T.1
-
3
-
-
0001318726
-
Sobolev inequalities in disguise
-
Bakry D., Coulhon T., Ledoux M., Saloff-Coste L.: Sobolev inequalities in disguise. Indiana Univ. Math. J. 44, 1033-1074 (1995).
-
(1995)
Indiana Univ. Math. J.
, vol.44
, pp. 1033-1074
-
-
Bakry, D.1
Coulhon, T.2
Ledoux, M.3
Saloff-Coste, L.4
-
4
-
-
0000759151
-
Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
-
Beckner W.: Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality. Ann. Math. 138, 213-242 (1993).
-
(1993)
Ann. Math.
, vol.138
, pp. 213-242
-
-
Beckner, W.1
-
5
-
-
1842637472
-
Geometric proof of Nash's inequality
-
Beckner, W.: Geometric proof of Nash's inequality. Int. Math. Res. Not. 67-71 (1998).
-
(1998)
Int. Math. Res. Not
, pp. 67-71
-
-
Beckner, W.1
-
6
-
-
0033249421
-
Geometric asymptotics and the logarithmic Sobolev inequality
-
Beckner W.: Geometric asymptotics and the logarithmic Sobolev inequality. Forum Math. 11, 105-137 (1999).
-
(1999)
Forum Math.
, vol.11
, pp. 105-137
-
-
Beckner, W.1
-
7
-
-
39949084937
-
Nash type inequalities for fractional powers of non-negative self-adjoint operators
-
Bendikov A. D., Maheux P.: Nash type inequalities for fractional powers of non-negative self-adjoint operators. Trans. Am. Math. Soc. 359, 3085-3097 (2007).
-
(2007)
Trans. Am. Math. Soc.
, vol.359
, pp. 3085-3097
-
-
Bendikov, A.D.1
Maheux, P.2
-
8
-
-
84945016371
-
Minimal rearrangements of Sobolev functions
-
Brothers J. E., Ziemer W. P.: Minimal rearrangements of Sobolev functions. J. Reine Angew. Math. 384, 153-179 (1988).
-
(1988)
J. Reine Angew. Math.
, vol.384
, pp. 153-179
-
-
Brothers, J.E.1
Ziemer, W.P.2
-
10
-
-
0037091874
-
p-Busemann-Petty centroid inequality
-
p-Busemann-Petty centroid inequality. Adv. Math. 167, 128-141 (2002).
-
(2002)
Adv. Math.
, vol.167
, pp. 128-141
-
-
Campi, S.1
Gronchi, P.2
-
11
-
-
0000273265
-
Superadditivity of Fisher's information and logarithmic Sobolev inequalities
-
Carlen E. A.: Superadditivity of Fisher's information and logarithmic Sobolev inequalities. J. Funct. Anal. 101, 194-211 (1991).
-
(1991)
J. Funct. Anal.
, vol.101
, pp. 194-211
-
-
Carlen, E.A.1
-
12
-
-
84963043487
-
Sharp constant in Nash's inequality
-
Carlen, E. A., Loss, M.: Sharp constant in Nash's inequality. Int. Math. Res. Not. 213-215 (1993).
-
(1993)
Int. Math. Res. Not
, pp. 213-215
-
-
Carlen, E.A.1
Loss, M.2
-
13
-
-
0001611867
-
On the existence of an extremal function for an inequality of J. Moser
-
Carleson L., Chang S. Y. A.: On the existence of an extremal function for an inequality of J. Moser. Bull. Sci. Math. 110, 113-127 (1986).
-
(1986)
Bull. Sci. Math.
, vol.110
, pp. 113-127
-
-
Carleson, L.1
Chang, S.Y.A.2
-
14
-
-
0039127823
-
Rearrangements of functions and convergence in Orlicz spaces
-
Chiti G.: Rearrangements of functions and convergence in Orlicz spaces. Appl. Anal. 9, 23-27 (1979).
-
(1979)
Appl. Anal.
, vol.9
, pp. 23-27
-
-
Chiti, G.1
-
15
-
-
33746888293
-
p-Minkowski problem and the Minkowski problem in centroaffine geometry
-
p-Minkowski problem and the Minkowski problem in centroaffine geometry. Adv. Math. 205, 33-83 (2006).
-
(2006)
Adv. Math.
, vol.205
, pp. 33-83
-
-
Chou, K.-S.1
Wang, X.-J.2
-
16
-
-
0012940631
-
Second-order derivatives and rearrangements
-
Cianchi A.: Second-order derivatives and rearrangements. Duke Math. J. 105, 355-385 (2000).
-
(2000)
Duke Math. J.
, vol.105
, pp. 355-385
-
-
Cianchi, A.1
-
17
-
-
23244434397
-
Moser-Trudinger inequalities without boundary conditions and isoperimetric problems
-
Cianchi A.: Moser-Trudinger inequalities without boundary conditions and isoperimetric problems. Indiana Univ. Math. J. 54, 669-705 (2005).
-
(2005)
Indiana Univ. Math. J.
, vol.54
, pp. 669-705
-
-
Cianchi, A.1
-
18
-
-
38849154370
-
Moser-Trudinger trace inequalities
-
Cianchi A.: Moser-Trudinger trace inequalities. Adv. Math. 217, 2005-2044 (2008).
-
(2008)
Adv. Math.
, vol.217
, pp. 2005-2044
-
-
Cianchi, A.1
-
19
-
-
39649092311
-
A quantitative Pólya-Szegö principle
-
Cianchi A., Esposito L., Fusco N., Trombetti C.: A quantitative Pólya-Szegö principle. J. Reine Angew. Math. 614, 153-189 (2008).
-
(2008)
J. Reine Angew. Math.
, vol.614
, pp. 153-189
-
-
Cianchi, A.1
Esposito, L.2
Fusco, N.3
Trombetti, C.4
-
20
-
-
0036027235
-
Functions of bounded variation and rearrangements
-
Cianchi A., Fusco N.: Functions of bounded variation and rearrangements. Arch. Ration. Mech. Anal. 165, 1-40 (2002).
-
(2002)
Arch. Ration. Mech. Anal.
, vol.165
, pp. 1-40
-
-
Cianchi, A.1
Fusco, N.2
-
21
-
-
33646527152
-
Steiner symmetric extremals in Pólya-Szegö type inequalities
-
Cianchi A., Fusco N.: Steiner symmetric extremals in Pólya-Szegö type inequalities. Adv. Math. 203, 673-728 (2006).
-
(2006)
Adv. Math.
, vol.203
, pp. 673-728
-
-
Cianchi, A.1
Fusco, N.2
-
22
-
-
85065359909
-
Minimal rearrangements, strict convexity and minimal points
-
Cianchi A., Fusco N.: Minimal rearrangements, strict convexity and minimal points. Appl. Anal. 85, 67-85 (2006).
-
(2006)
Appl. Anal.
, vol.85
, pp. 67-85
-
-
Cianchi, A.1
Fusco, N.2
-
23
-
-
70350389542
-
Affine Moser-Trudinger and Morrey-Sobolev inequalities
-
Cianchi A., Lutwak E., Yang D., Zhang G.: Affine Moser-Trudinger and Morrey-Sobolev inequalities. Calc. Var. Partial Differ. Equ. 36, 419-436 (2009).
-
(2009)
Calc. Var. Partial Differ. Equ.
, vol.36
, pp. 419-436
-
-
Cianchi, A.1
Lutwak, E.2
Yang, D.3
Zhang, G.4
-
24
-
-
0039248898
-
Best constants for Moser-Trudinger inequalities on the Heisenberg group
-
Cohn W. S., Lu G.: Best constants for Moser-Trudinger inequalities on the Heisenberg group. Indiana Univ. Math. J. 50, 1567-1591 (2001).
-
(2001)
Indiana Univ. Math. J.
, vol.50
, pp. 1567-1591
-
-
Cohn, W.S.1
Lu, G.2
-
25
-
-
1242299735
-
A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities
-
Cordero-Erausquin D., Nazaret B., Villani C.: A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Adv. Math. 182, 307-332 (2004).
-
(2004)
Adv. Math.
, vol.182
, pp. 307-332
-
-
Cordero-Erausquin, D.1
Nazaret, B.2
Villani, C.3
-
26
-
-
0036710614
-
Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
-
Del Pino M., Dolbeault J.: Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions. J. Math. Pures Appl. 81, 847-875 (2002).
-
(2002)
J. Math. Pures Appl.
, vol.81
, pp. 847-875
-
-
Del Pino, M.1
Dolbeault, J.2
-
28
-
-
0345356496
-
Convex symmetrization and Pólya-Szegö inequality
-
Esposito L., Trombetti C.: Convex symmetrization and Pólya-Szegö inequality. Nonlinear Anal. 56, 43-62 (2004).
-
(2004)
Nonlinear Anal.
, vol.56
, pp. 43-62
-
-
Esposito, L.1
Trombetti, C.2
-
30
-
-
0000562793
-
Normal and integral currents
-
Federer H., Fleming W.: Normal and integral currents. Ann. Math. 72, 458-520 (1960).
-
(1960)
Ann. Math.
, vol.72
, pp. 458-520
-
-
Federer, H.1
Fleming, W.2
-
31
-
-
7244242195
-
Convex symmetrization: the equality case in the Pólya-Szegö inequality
-
Ferone A., Volpicelli R.: Convex symmetrization: the equality case in the Pólya-Szegö inequality. Calc. Var. Part. Differ. Equ. 21, 259-272 (2004).
-
(2004)
Calc. Var. Part. Differ. Equ.
, vol.21
, pp. 259-272
-
-
Ferone, A.1
Volpicelli, R.2
-
32
-
-
51249167010
-
Extremal functions for Trudinger-Moser inequality in 2 dimensions
-
Flucher M.: Extremal functions for Trudinger-Moser inequality in 2 dimensions. Comment. Math. Helvetici 67, 471-497 (1992).
-
(1992)
Comment. Math. Helvetici
, vol.67
, pp. 471-497
-
-
Flucher, M.1
-
33
-
-
0035997406
-
The Brunn-Minkowksi inequality
-
Gardner R. J.: The Brunn-Minkowksi inequality. Bull. Am. Math. Soc. (N. S.) 39, 355-405 (2002).
-
(2002)
Bull. Am. Math. Soc. (N.S.)
, vol.39
, pp. 355-405
-
-
Gardner, R.J.1
-
34
-
-
0001429116
-
Logarithmic Sobolev inequalities
-
Gross L.: Logarithmic Sobolev inequalities. Am. J. Math. 97, 1061-1083 (1975).
-
(1975)
Am. J. Math.
, vol.97
, pp. 1061-1083
-
-
Gross, L.1
-
40
-
-
0003269816
-
Rearrangements and convexity of level sets in PDE
-
Springer, Berlin
-
Kawohl, B.: Rearrangements and convexity of level sets in PDE. In: Lecture Notes in Mathematics, vol. 1150. Springer, Berlin (1985).
-
(1985)
Lecture Notes in Mathematics
, vol.1150
-
-
Kawohl, B.1
-
41
-
-
0013001564
-
On the isoperimetric nature of a rearrangement inequality and its consequences for some variational problems
-
Kawohl B.: On the isoperimetric nature of a rearrangement inequality and its consequences for some variational problems. Arch. Ration. Mech. Anal. 94, 227-243 (1986).
-
(1986)
Arch. Ration. Mech. Anal.
, vol.94
, pp. 227-243
-
-
Kawohl, B.1
-
42
-
-
44449109764
-
-
Hackensack: World Scientific, Series in Analysis
-
Kesavan S.: Symmetrization and Applications. Series in Analysis 3. World Scientific, Hackensack (2006).
-
(2006)
Symmetrization and Applications
, vol.3
-
-
Kesavan, S.1
-
43
-
-
0000639280
-
Isoperimetry and Gaussian analysis
-
(Saint-Flour, 1994). Lecture Notes in Mathematics, Springer, Berlin
-
Ledoux, M.: Isoperimetry and Gaussian analysis. In: Lectures on Probability Theory and Statistics (Saint-Flour, 1994). Lecture Notes in Mathematics, vol. 1648, pp. 165-294. Springer, Berlin (1996).
-
(1996)
Lectures on Probability Theory and Statistics
, vol.1648
, pp. 165-294
-
-
Ledoux, M.1
-
45
-
-
21344447692
-
Extremal functions for Moser's inequality
-
Lin K. C.: Extremal functions for Moser's inequality. Trans. Am. Math. Soc. 348, 2663-2671 (1996).
-
(1996)
Trans. Am. Math. Soc.
, vol.348
, pp. 2663-2671
-
-
Lin, K.C.1
-
46
-
-
0042575606
-
Ellipsoids and matrix-valued valuations
-
Ludwig M.: Ellipsoids and matrix-valued valuations. Duke Math. J. 119, 159-188 (2003).
-
(2003)
Duke Math. J.
, vol.119
, pp. 159-188
-
-
Ludwig, M.1
-
47
-
-
26444584569
-
Minkowski valuations
-
Ludwig M.: Minkowski valuations. Trans. Am. Math. Soc. 357, 4191-4213 (2005).
-
(2005)
Trans. Am. Math. Soc.
, vol.357
, pp. 4191-4213
-
-
Ludwig, M.1
-
48
-
-
77957697204
-
A classification of SL(n) invariant valuations
-
Ludwig M., Reitzner M.: A classification of SL(n) invariant valuations. Ann. Math. 172, 1219-1267 (2010).
-
(2010)
Ann. Math.
, vol.172
, pp. 1219-1267
-
-
Ludwig, M.1
Reitzner, M.2
-
49
-
-
79953242509
-
Sharp convex Lorentz-Sobolev inequalities
-
doi: 10. 1007/s00208-010-055-x
-
Ludwig, M., Xiao, J., Zhang, G.: Sharp convex Lorentz-Sobolev inequalities. Math. Ann., 29. doi: 10. 1007/s00208-010-055-x.
-
Math. Ann
, vol.29
-
-
Ludwig, M.1
Xiao, J.2
Zhang, G.3
-
50
-
-
0001874829
-
On some affine isoperimetric inequalities
-
Lutwak E.: On some affine isoperimetric inequalities. J. Differ. Geom. 23, 1-13 (1986).
-
(1986)
J. Differ. Geom.
, vol.23
, pp. 1-13
-
-
Lutwak, E.1
-
51
-
-
84972508818
-
The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem
-
Lutwak E.: The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem. J. Differ. Geom. 38, 131-150 (1993).
-
(1993)
J. Differ. Geom.
, vol.38
, pp. 131-150
-
-
Lutwak, E.1
-
52
-
-
0030600832
-
The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
-
Lutwak E.: The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas. Adv. Math. 118, 244-294 (1996).
-
(1996)
Adv. Math.
, vol.118
, pp. 244-294
-
-
Lutwak, E.1
-
53
-
-
84972497535
-
On the regularity of solutions to a generalization of the Minkowski problem
-
Lutwak E., Oliker V.: On the regularity of solutions to a generalization of the Minkowski problem. J. Differ. Geom. 41, 227-246 (1995).
-
(1995)
J. Differ. Geom.
, vol.41
, pp. 227-246
-
-
Lutwak, E.1
Oliker, V.2
-
55
-
-
0034664274
-
A new ellipsoid associated with convex bodies
-
Lutwak E., Yang D., Zhang G.: A new ellipsoid associated with convex bodies. Duke Math. J. 104, 375-390 (2000).
-
(2000)
Duke Math. J.
, vol.104
, pp. 375-390
-
-
Lutwak, E.1
Yang, D.2
Zhang, G.3
-
59
-
-
0001363544
-
Classes of domains and imbedding theorems for function spaces
-
Maz'ya V. G.: Classes of domains and imbedding theorems for function spaces. Dokl. Akad. Nauk. SSSR 133, 527-530 (1960).
-
(1960)
Dokl. Akad. Nauk. SSSR
, vol.133
, pp. 527-530
-
-
Maz'ya, V.G.1
-
60
-
-
0001173833
-
A sharp form of an inequality by Trudinger
-
Moser J.: A sharp form of an inequality by Trudinger. Indiana Univ. Math. J. 20, 1077-1092 (1970).
-
(1970)
Indiana Univ. Math. J.
, vol.20
, pp. 1077-1092
-
-
Moser, J.1
-
61
-
-
0002344844
-
Isoperimetric problems
-
(Univ. Oklahoma 1971), University of Oklahoma
-
Petty, C. M.: Isoperimetric problems. In: Proc. Conf. Convexity and Combinatorial Geometry (Univ. Oklahoma 1971), pp. 26-41. University of Oklahoma (1972).
-
(1972)
Proc. Conf. Convexity and Combinatorial Geometry
, pp. 26-41
-
-
Petty, C.M.1
-
62
-
-
0003458682
-
Isoperimetric inequalities in mathematical physics
-
Princeton University Press
-
Pólya, G., Szegö, G.: Isoperimetric inequalities in mathematical physics. Ann. Math. Stud. 27. Princeton University Press (1951).
-
(1951)
Ann. Math. Stud
, vol.27
-
-
Pólya, G.1
Szegö, G.2
-
65
-
-
12944295719
-
Some inequalities satisfied by the quantities of information of Fisher and Shannon
-
Stam A. J.: Some inequalities satisfied by the quantities of information of Fisher and Shannon. Inform. Control 2, 255-269 (1959).
-
(1959)
Inform. Control
, vol.2
, pp. 255-269
-
-
Stam, A.J.1
-
66
-
-
34250392866
-
Best constant in Sobolev inequality
-
Talenti G.: Best constant in Sobolev inequality. Ann. Math. Pure Appl. 110, 353-372 (1976).
-
(1976)
Ann. Math. Pure Appl.
, vol.110
, pp. 353-372
-
-
Talenti, G.1
-
67
-
-
0039007378
-
On isoperimetric theorems in mathematical physics
-
P. M. Gruber and J. M. Wills (Eds.), Amsterdam: North-Holland
-
Talenti G.: On isoperimetric theorems in mathematical physics. In: Gruber, P. M., Wills, J. M. (eds) Handbook of Convex Geometry, North-Holland, Amsterdam (1993).
-
(1993)
Handbook of Convex Geometry
-
-
Talenti, G.1
-
68
-
-
0039985113
-
Inequalities in rearrangement invariant function spaces
-
In: Krbec, M., Kufner, A., Opic, B., Rákosnik, J. (eds.), Prometheus, Prague
-
Talenti, G.: Inequalities in rearrangement invariant function spaces. In: Krbec, M., Kufner, A., Opic, B., Rákosnik, J. (eds.) Nonlinear Analysis, Function Spaces and Applications, vol. 5, pp. 177-230. Prometheus, Prague (1994).
-
(1994)
Nonlinear Analysis, Function Spaces and Applications
, vol.5
, pp. 177-230
-
-
Talenti, G.1
-
69
-
-
0000453612
-
On imbeddings into Orlicz spaces and some applications
-
Trudinger N. S.: On imbeddings into Orlicz spaces and some applications. J. Math. Mech. 17, 473-483 (1967).
-
(1967)
J. Math. Mech.
, vol.17
, pp. 473-483
-
-
Trudinger, N.S.1
-
70
-
-
84968502357
-
Logarithmic Sobolev inequalities for the heat-diffusion semigroup
-
Weissler F. B.: Logarithmic Sobolev inequalities for the heat-diffusion semigroup. Trans. Am. Math. Soc. 237, 255-269 (1978).
-
(1978)
Trans. Am. Math. Soc.
, vol.237
, pp. 255-269
-
-
Weissler, F.B.1
-
71
-
-
33947598128
-
The sharp Sobolev and isoperimetric inequalities split twice
-
Xiao J.: The sharp Sobolev and isoperimetric inequalities split twice. Adv. Math. 211, 417-435 (2007).
-
(2007)
Adv. Math.
, vol.211
, pp. 417-435
-
-
Xiao, J.1
-
72
-
-
0001846041
-
The affine Sobolev inequality
-
Zhang G.: The affine Sobolev inequality. J. Differ. Geom. 53, 183-202 (1999).
-
(1999)
J. Differ. Geom.
, vol.53
, pp. 183-202
-
-
Zhang, G.1
|