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math.AP2026
Sobolev Inequalities and the Existence of Solutions to Degenerate -Poisson Equations
David Cruz-Uribe, Feyza Dal, Scott Rodney
In this paper we study an equivalence between the existence of a Sobolev inequality without gain, \[\|φ\|_{L^p(v,Ω)} \leq S(p,1) \| \sqrt{Q}\nabla φ\|_{L^p(Ω)},\] that holds for sm…
math.AP2026
Degenerate Sobolev and Poincaré inequalities via extrapolation
David Cruz-Uribe, Feyza Elif Dal, Scott Rodney
In this paper we prove matrix weighted Sobolev and Poincaré inequalities using techniques derived from the theory of Rubio de Francia extrapolation. Given weights and a sym…