Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Akrivou Eleni-Ioanna
Supervisors info:
Γεράσιμος Μπαρμπάτης Καθηγητής Τμήμα Μαθηματικών ΕΚΠΑ
Original Title:
Hardy-Sobolev Inequalities
Translated title:
Hardy-Sobolev Inequalities
Summary:
In the present work we study two types of the Hardy-Sobolev inequality, the one involving distance to the origin and the other involving distance to the boundary. For the Hardy-Sobolev inequality involving distance to the origin, we also obtain the sharp constant. We relate this inequality to a limiting Caffarelli-Kohn-Nirenberg inequality and we prove that they are equivalent. Particularly in three dimensions the sharp constant coincides with the best Sobolev constant. Similarly, for the Hardy-Sobolev inequality involving distance to the boundary we prove that the sharp constant of the inequality on the three dimensional upper half space is given by the Sobolev constant.
In both cases we added a Sobolev term with the best constant on the Hardy inequality which has already a best constant.
Main subject category:
Science
Keywords:
Inequalities, Hardy, Sobolev
