منابع مشابه
An isoperimetric inequality for logarithmic capacity
We prove a sharp lower bound of the form capE ≥ (1/2)diamE · Ψ(areaE/((π/4)diam 2E)) for the logarithmic capacity of a compact connected planar set E in terms of its area and diameter. Our lower bound includes as special cases G. Faber’s inequality capE ≥ diamE/4 and G. Pólya’s inequality capE ≥ (areaE/π)1/2. We give explicit formulations, functions of (1/2)diamE, for the extremal domains which...
متن کاملAn isoperimetric inequality for logarithmic capacity of polygons
We verify an old conjecture of G. Pólya and G. Szegő saying that the regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area.
متن کاملLogarithmic Sobolev inequality revisited
r é s u m é Nous donnons une nouvelle caractérisation de l’inégalité de Sobolev logarithmique. © 2017 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.
متن کاملLogarithmic Sobolev Trace Inequality
A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality. Logarithmic Sobolev inequalities capture the spirit of classical Sobolev inequalities with the logarithm function replacing powers, and they can be considered as limiting cases of...
متن کاملLogarithmic Sobolev inequality for diffusion semigroups
Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincaré or logarithmic Sobolev inequalities. Moreover an alternative method using the optimal mass transportation, is also given to obtain the logarithmic Sobolev inequality. Mathematics Subject Classification (2000) : Primary 35B40, 35K10, 60J60.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1961
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1961.11.313