Sharp remainder of the Poincare inequality for Baouendi-Grushin vector fields
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, cilt.16, sa.3, 2023 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16 Sayı: 3
- Basım Tarihi: 2023
- Doi Numarası: 10.1142/s1793557123500419
- Dergi Adı: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
- Anahtar Kelimeler: Poincare inequalitiy, Baouendi-Grushin operator, eigenfunction, blow-up solution, HARDY INEQUALITIES, BLOW-UP, EQUATIONS, NONEXISTENCE, THEOREMS, OPERATOR
- Süleyman Demirel Üniversitesi Adresli: Hayır
Özet
In this note, we establish a sharp remainder formula for the Poincare inequality for the Baouendi-Crushin vector fields. We give a simple proof for it without using the variational principle. As an application, we obtain a blow-up result for solutions to the Dirichlet initial-boundary value problem for the Baouendi-Grushin heat operator.