Asymmetric affine Lp Sobolev inequalities
By Christoph Haberl, Franz E. Schuster. 2009
268 citations recorded by the source corpus.
Abstract A new sharp affine L p Sobolev inequality for functions on R n is established. This inequality strengthens and implies the previously known affine L p Sobolev inequality which in turn is stronger than the classical L p Sobolev inequality.
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/cba2ee8fae2a4c381c5736a7a34b616f601c5e64
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In Applied Mathematics
- Yiming Zhao
- Deping Ye
- Yong Huang
- Monika Ludwig
- Deane Yang
- Gaoyong Zhang
- Erwin Lutwak
- Christoph Haberl
In Numerical Analysis
- Yiming Zhao
- Monika Ludwig
- Gaoyong Zhang
- Deane Yang
- Van Hoang Nguyen
- Erwin Lutwak
- Christoph Haberl
- Lukas Parapatits
Citations in the corpus
- Shadow systems of asymmetric Lp zonotopes (2013, unknown): “[14–16]).”
- The dual Minkowski problem for negative indices (2017, methodology): “See, e.g., Haberl [19], Haberl & Ludwig [20] ,Haberl & Parapatits [21,22], Ludwig [27,28], Ludwig & Reitzner [29], Schuster [39, 40], Schuster & Wannerer [41] and the references therein for important valuations and their characterizations in the theory of convex bodies.”
- 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 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 Surface Area Measures (2014, methodology): “Solutions to the Lp Minkowski problem were crucial for the proofs of affine versions of the Pólya-Szegö principle and new affine Sobolev inequalities (see [8, 17,18,28,30]).”
- Dual Orlicz-Brunn-Minkowski theory (2014, background): “, Ludwig [30], Haberl and Schuster [23], and Ludwig and Reitzner [33].”
- Orlicz centroid bodies (2010, background): “The works of Haberl and Schuster [21] (see also [22]), Ludwig and Reitzner [32], and Ludwig [31] have demonstrated the clear need to move beyond the Lp Brunn-Minkowski theory to what we are calling an Orlicz Brunn-Minkowski theory.”
- THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES (2013, unknown): “See, for example, [4], [13], [14], [21], [22], [23], [24], [26], and [35].”
- An asymmetric affine Pólya–Szegö principle (2012, background): “In [36] it was shown that (6) E p (f) ≤ Ep(f), with equality if and only if ‖Du f‖p is an even function on Sn−1.”
- Minkowski valuations intertwining the special linear group (2012, result): “Recently, her results led to strengthenings and generalizations of several affine isoperimetric and Sobolev inequalities [27,28,47,48].”