Degenerate Sobolev inequalities from the classical Sobolev inequality

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

Analysis and Mathematical Physics, vol.15, no.3, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 3
  • Publication Date: 2025
  • Doi Number: 10.1007/s13324-025-01065-7
  • Journal Name: Analysis and Mathematical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Degenerate elliptic equations, Sobolev inequalities, Weighted Sobolev spaces
  • Yıldız Technical University Affiliated: Yes

Abstract

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).