The optimal Euclidean Lp-Sobolev logarithmic inequality

By Manuel del Pino, Jean Dolbeault. 2003

205 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5c26986a515ecece1a3015000bbbafd7cc489834

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In Applied Mathematics

1. Van Hoang Nguyen
2. Christoph Haberl
3. Franz E. Schuster
4. Monika Ludwig
5. Yiming Zhao
6. Jie Xiao
7. Chao Ji
8. Zoltán M. Balogh

In Mechanics of Materials

1. Christoph Haberl
2. Franz E. Schuster
3. Chao Ji
4. Alexandru Krist'aly
5. Van Hoang Nguyen
6. Jie Xiao
7. A. Szulkin

Citations in the corpus

• An asymmetric affine Pólya–Szegö principle (2012, methodology): “The natural problem to find a sharp L p analogue of inequality (44) was solved by Ledoux [43] for p = 1 and recently by Del Pino and Dolbeault [27] for 1 < p < n: If f ∈ W 1,p(Rn), with 1 ≤ p < n, such that ‖ f ‖p = 1, then ∫”
• A logarithmic Schrödinger equation with asymptotic conditions on the potential (2015, background): “.1 inequality (2.4) must be replaced by a p-logarithmic Sobolev inequality. A suitable version for our purposes is Z RN |u|p log|u|p dx ≤ N p log(C pk∇ukp), see the formula in the middle of p. 153 in [8]. In the convergence part of the proof of Proposition 3.1, a formula corresponding to (3.3) is Z ”
• New approach to the affine P\'olya-Szeg\"o principle and the stability version of the affine Sobolev inequality (2015, methodology): “4) is proved by combining the general affine PólyaSzegö principle and the classical Gagliardo-Nirenberg inequality [14, 15, 16].”
• Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature (2020, background): “Sharp Gagliardo-Nirenberg inequalities on Rn are known after Del Pino and Dolbeault [22] and Cordero-Erausquin, Nazaret and Villani [19].”
• Sharp weighted Sobolev and Gagliardo–Nirenberg inequalities on half‐spaces via mass transport and consequences (2013, methodology): “On R, sharp Lp−logarithmic Sobolev inequalities for 1 ≤ p < n were proved first by Del Pino and Dolbeault [14, 15] by considering the above mentioned limit of the sharp GN inequalities.”
• Multiple solutions to logarithmic Schrödinger equations with periodic potential (2014, unknown): “[13] and the references therein.”