Affine Moser–Trudinger and Morrey–Sobolev inequalities

By Andrea Cianchi, Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2009

227 citations recorded by the source corpus.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/68bde4c618294b1e4b8245a5403daca919d11940

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In Applied Mathematics

1. Yiming Zhao
2. Deping Ye
3. Yong Huang
4. Deane Yang
5. Gaoyong Zhang
6. K. Boroczky
7. Erwin Lutwak
8. Monika Ludwig

Citations in the corpus

• 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]).”
• Sharp Singular Trudinger–Moser Inequalities in Lorentz–Sobolev Spaces (2016, background): “For instance, we refer the reader to [10, 25, 32] for the sharp Trudinger–Moser inequality with mean value zero, to [3] for the singular Trudinger–Moser inequality and to [12] for the sharp affine Trudinger–Moser inequalities.”
• Functional Versions of Lp-Affine Surface Area and Entropy Inequalities (2014, unknown): “In recent years, functional versions of several isoperimetric type inequalities from convex geometry have been established [15, 25, 32, 35, 36, 46].”
• Sharp convex Lorentz–Sobolev inequalities (2011, unknown): “Within the Lp Brunn-Minkowski theory (see [10,13–15,30–32,35,36,39–42,44–49,61,67,69– 71, 74]), the natural extension of integral affine surface area is the Lp integral affine surface area Φp (see Section 5.”
• The logarithmic Minkowski problem (2012, unknown): “…of the even L p -Minkowski problem was a critical ingredient that allowed the authors of [44] to extend the affine Sobolev inequality [63] and obtain the L p affine Sobolev inequality, and later enabled Cianchi et al. [12] to establish the affine Moser-Trudinger and the affine Morrey-Sobolev inequalities.”
• Minkowski valuations intertwining the special linear group (2012, unknown): “, [17, 21,27,45,61,62,66]).”
• General affine surface areas (2009, background): “During the past decade and a half, there has been an explosive growth of an Lp extension of the classical Brunn Minkowski theory (see, for example, [6–8,15–17,24,25,31,34–38,46,47]).”
• On the L dual Minkowski problem (2018, background): “, Cianchi, Lutwak, Yang & Zhang [20], Lutwak, Yang & Zhang [52], and Zhang [66].”