13,941 research outputs found
On weighted Hardy inequalities for non-increasing sequences
A result of Bennett and Grosse-Erdmann characterizes the weights for which
the corresponding weighted Hardy inequality holds on the cone of non-negative,
non-increasing sequences and a bound for the best constant is given. In this
paper, we improve the bound for .Comment: 6 page
Sums of Powers and Majorization
We study certain sequences involving sums of powers of positive integers and in connection
with this, we give examples to show that power majorization does not imply majorization
The classical overdetermined Serrin problem
In this survey we consider the classical overdetermined problem which was
studied by Serrin in 1971. The original proof relies on Alexandrov's moving
plane method, maximum principles, and a refinement of Hopf's boundary point
Lemma. Since then other approaches to the same problem have been devised. Among
them we consider the one due to Weinberger which strikes for the elementary
arguments used and became very popular. Then we discuss also a duality approach
involving harmonic functions, a shape derivative approach and a purely integral
approach, all of them not relying on maximum principle. For each one we
consider pros and cons as well as some generalizations
- …