Weighted rellich type inequalities related to baouendi-grushin operators

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KÖMBE İ., YENER A.

Proceedings of the American Mathematical Society, cilt.145, sa.11, ss.4845-4857, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 145 Sayı: 11
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1090/proc/13730
  • Dergi Adı: Proceedings of the American Mathematical Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4845-4857
  • Anahtar Kelimeler: Baouendi-Grushin vector fields, weighted Rellich inequality, two-weight Rellich inequality, remainder term
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

We find a simple sufficient criterion on a pair of nonnegative weight functions a (x, y) and b (x, y) in ℝm+k so that the general weighted Lp Rellich type inequality (Formula presented) holds for all u ∈ C0∞(ℝm+k). Here Δγ = Δx + |x|2γΔy is the Baouendi-Grushin operator, γ > 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 ℝm+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 Ω in ℝm+k via a nonlinear differential inequality.