Steklov-type 1D inequalities (a survey)

TL;DR

This survey reviews classical and recent results on sharp constants and extremal functions in one-dimensional functional inequalities, highlighting key developments and open problems in the field.

Contribution

It compiles and discusses recent advances and classical results on sharp constants and symmetry properties of extremal functions in 1D inequalities.

Findings

Summary of sharp constants in 1D inequalities

Analysis of symmetry and asymmetry of extremal functions

Identification of open problems and future directions

Abstract

We give a survey of classical and recent results on sharp constants and symmetry/asymmetry of extremal functions in $1$-dimensional functional inequalities.