Weighted rellich type inequalities related to baouendi-grushin operators
Küçük Resim Yok
Tarih
2017
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
American Mathematical Society
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
We find a simple sufficient criterion on a pair of nonnegative weight functions a (x, y) and b (x, y) in ?m+k so that the general weighted Lp Rellich type inequality (Formula presented) holds for all u ? C0?(?m+k). Here ?? = ?x + |x|2??y is the Baouendi-Grushin operator, ? > 0, m, k ? 1 and p > 1. It is important to point out here that our approach is constructive in the sense that it allows us to retrieve already established weighted sharp Rellich type inequalities as well as to get other new results with an explicit constant on ?m+k. We also obtain a sharp Lp Rellich type inequality that connects first to second order derivatives and several new two-weight Rellich type inequalities with remainder terms on smooth bounded domains ? in ?m+k via a nonlinear differential inequality. © 2017 American Mathematical Society.
Açıklama
Anahtar Kelimeler
Baouendi-Grushin vector fields, Remainder term, Two-weight Rellich inequality, Weighted Rellich inequality
Kaynak
Proceedings of the American Mathematical Society
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
145
Sayı
11
