Degenerate Sobolev inequalities from the classical Sobolev inequality

Cruz-Uribe, David; Dal, Feyza; Rodney, Scott; ZEREN, Yusuf

doi:10.1007/s13324-025-01065-7

Degenerate Sobolev inequalities from the classical Sobolev inequality

Cruz-Uribe D., Dal F. E., Rodney S., ZEREN Y.

Analysis and Mathematical Physics, cilt.15, sa.3, 2025 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 15 Sayı: 3
Basım Tarihi: 2025
Doi Numarası: 10.1007/s13324-025-01065-7
Dergi Adı: Analysis and Mathematical Physics
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
Anahtar Kelimeler: Degenerate elliptic equations, Sobolev inequalities, Weighted Sobolev spaces
Yıldız Teknik Üniversitesi Adresli: Evet

Özet

We prove a degenerate Sobolev inequality of the form (Formula presented.) where Q is a matrix function whose smallest eigenvalue is bounded below by a constant multiple of K-2p′. As an application, we prove the exponential integrability of solutions of the Dirichlet problem for -K-1div(Q∇u)=f, f∈L∞(K,Ω), building upon recent results in Cruz-Uribe, MacDonald, and Rodney (2024).