Sharp Affine LP Sobolev Inequalities

By Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2002

350 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/37d1803691a58b5b0769a3b89fc69f17859331d1

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Valuations on Sobolev spaces (2012, background): “Moreover, the optimal Sobolev body has proved to be critical in recent results on affine isoperimetric inequalities (see [13, 24, 40, 44, 45, 59, 60]).”
The $L_p$-Aleksandrov problem for $L_p$-integral curvature (2018, methodology): “In [11, 21, 37, 39, 54] affine Sobolev inequalities were obtained by using the solution of the Minkowski problem and the Lp-Minkowski problem (together with Lpaffine isoperimetric inequalities from [36, 20]).”
The dual Minkowski problem for negative indices (2017, methodology): “The solution to the Lp Minkowski problem has proven to be essential in establishing different analytic affine isoperimetric inequalities (see, for example, Haberl & Schuster [23], LYZ [34], Wang [44], and Zhang [45]).”
GL(n) contravariant Minkowski valuations (2012, background): “This remarkable inequality also forms the geometric core of the affine Zhang–Sobolev inequality [26, 42] which strengthens and directly implies the classical Sobolev inequality.”
THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES (2013, neutral): “See, for example, [4], [13], [14], [21], [22], [23], [24], [26], and [35].”
Volume Inequalities for Subspaces of L p (2004, neutral): “, [7], [8], [9], [15], [16], [17], [22], [23], [24], [25], [26], [27], [28], [30], [29], [31], [32], [33], [34], [35], [39], [43], [44], [45], [46], [48]) motivated the search for a direct approach to establishing these reverse inequalities.”
On the L dual Minkowski problem (2018, background): “, Cianchi, Lutwak, Yang & Zhang [20], Lutwak, Yang & Zhang [52], and Zhang [66].”
Existence of solutions to the even dual Minkowski problem (2018, methodology): “The following is a special case of the variational formula for the dual quermassintegral established in Huang-LYZ [32].”
The Dual Orlicz–Minkowski Problem (2017, methodology): “For instance, it has been used to establish the sharp affine Sobolev inequalities [7, 16, 32, 52].”
Valuations and Busemann{Petty Type Problems (2008, neutral): “[9,10,44–47].”
General $L_p$ affine isoperimetric inequalities (2008, background): “This extension is the geometric core of a sharp affine Lp Sobolev inequality which is significantly stronger than the classical Lp Sobolev inequality, see [32, 52].”