Pointwise symmetrization inequalities for Sobolev functions and applications
By Joaquim Martín, Mario Milman. 2009
56 citations recorded by the source corpus.
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c58fba381914a8c8a264cb077f06dee2fe7968f9
How researchers see this paper
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In Applied Mathematics
- Amiran Gogatishvili
- Lenka Slav'ikov'a
- L. Pick
- Andrea Cianchi
- Maria Rosaria Formica
- Giovanni Mancini
- K. Sandeep
- Alberto Fiorenza
In Computational Theory and Mathematics
- Andrea Cianchi
- Amiran Gogatishvili
- C. Tintarev
- L. Pick
- K. Sandeep
- Alberto Fiorenza
- Giovanni Mancini
- Maria Rosaria Formica
In Mathematical Physics
- Giovanni Mancini
- K. Sandeep
- Maria Rosaria Formica
- Lenka Slav'ikov'a
- L. Pick
- Andrea Cianchi
- Amiran Gogatishvili
- Alberto Fiorenza
Citations in the corpus
- Higher-order Sobolev embeddings and isoperimetric inequalities (2013, result): “8 provide us with a characterization of Gaussian Sobolev embeddings which somewhat simplifies earlier results in a similar direction [33, 63].”
- Trudinger–Moser inequality in the hyperbolic space ℍN (2013, methodology): “By the standard rearrangement argument ([5,18]) applied on H equipped with its Riemannian measure, it suffices to consider the inequality only for radial functions on the Poincaré ball.”
- On grand and small Lebesgue and Sobolev spaces and some applications to PDE's (2018, background): “one has that Yp(0,1) ⊂ Lp(logL)p/2(0,1) , the exponent p/2 being optimal (see [126], where the authors answered positively a conjecture by Hans Triebel).”