Author

David Cruz-Uribe

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Preprint Sep 2026

Sobolev Inequalities and the Existence of Solutions to Degenerate $p$-Poisson Equations

In this paper we study an equivalence between the existence of a Sobolev inequality without gain, \[\|\varphi\|_{L^p(v,\Omega)} \leq S(p,1) \| \sqrt{Q}\nabla \varphi\|_{L^p(\Omega)},\] that holds for smooth functions of compact support and the existence of a degenerate weak solution $(u,\nabla u)\in QH^{1,p}_0(v,\Omega...

David Cruz-Uribe, F. Dal, S. Rodney · 0 citations

Preprint Aug 2026

Degenerate Sobolev and Poincar\'e inequalities via extrapolation

In this paper we prove matrix weighted Sobolev and Poincar\'e inequalities using techniques derived from the theory of Rubio de Francia extrapolation. Given weights $w,\,v$ and a symmetric non-negative definite matrix valued function $Q$ defined on a connected open subset $\Omega$ of $\mathbb{f}R^n$ that satisfies the...

David Cruz-Uribe, Feyza Elif Dal, S. Rodney · 2 citations