Isoperimetric functional inequalities via the maximum principle: the exterior differential systems approach. (English) Zbl 1405.42023
Baranov, Anton (ed.) et al., 50 years with Hardy spaces. A tribute to Victor Havin. Cham: Birkhäuser (ISBN 978-3-319-59077-6/hbk; 978-3-319-59078-3/ebook). Operator Theory: Advances and Applications 261, 281-305 (2018).
Summary: Our goal in this note is to give a unified approach to the solutions of a class of isoperimetric problems by relating them to the exterior differential systems studied by R. L. Bryant and P. A. Griffiths [Duke Math. J. 78, No. 3, 531–676 (1995; Zbl 0853.58005); J. Am. Math. Soc. 8, No. 3, 507–596 (1995; Zbl 0845.58004)].
For the entire collection see [Zbl 1393.30002].
For the entire collection see [Zbl 1393.30002].
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B35 | Function spaces arising in harmonic analysis |
| 47A30 | Norms (inequalities, more than one norm, etc.) of linear operators |
Keywords:
log-Sobolev inequality; Poincaré inequality; Bobkov’s inequality; Gaussian isoperimetry; semigroups; maximum principle; Monge-Ampère equations; exterior differential systems; backward heat equation; (B) theoremSoftware:
MathOverflowReferences:
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