Note on Friedrichs' inequality in N-star-shaped domains
نویسندگان
چکیده
منابع مشابه
Note on Star-shaped Sets
1. The aim of this note is to prove that if 717" is a compact subset of En and for some m every w-dimensional hyperplane through a fixed point pQEn intersects M along a nonempty acyclic set, lúm^n — 1, then M is star-shaped with respect to p, i.e., if aQM then the segment pa is contained in M. This theorem is a generalization of a theorem of Aumann [l]. We gave recently a proof of Aumann's theo...
متن کاملNondegeneracy of Harmonic Volumetric Parameterization on Star-shaped Domains
sectionHarmonic Volumetric Parameterization using MFS After the decomposition of a given object M , we get a set of star shapes {Mi}, each region being guarded by a point gi. Then we can parameterize each subregion onto a solid sphere. A key property that we will show shortly is that such a harmonic map is guaranteed to be bijective. The harmonic map can be computed using the method of fundamen...
متن کاملOn the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne
The equivalence between the inequalities of Babuška–Aziz and Friedrichs for sufficiently smooth bounded domains in the plane has been shown by Horgan and Payne 30 years ago. We prove that this equivalence, and the equality between the associated constants, is true without any regularity condition on the domain. For the Horgan–Payne inequality, which is an upper bound of the Friedrichs constant ...
متن کاملA Note on Fisher's Inequality
A design D consists of a family B1 , ..., Bb of subets, called blocks, of a finite set S=[P1 , ..., Pv] whose elements are called points or varieties. D is balanced or *-linked if every pair of points is contained in exactly * blocks. If, in addition, *>0 and no block contains all the points, then D is nontrivial, and if every block has the same cardinality k then D is a balanced incomplete-blo...
متن کاملA Note on Carleman’s Inequality
n=1 an, with the constant e best possible. There is a rich literature on many different proofs of Carleman’s inequality as well as its generalizations and extensions. We shall refer the readers to the survey articles [7] and [5] as well as the references therein for an account of Carleman’s inequality. From now on we will assume an ≥ 0 for n ≥ 1 and any infinite sum converges. Our goal in this ...
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: Journal of Mathematical Analysis and Applications
سال: 2016
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.10.046