4 papers · 1 filter
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…
The weak maximum principle for solutions of degenerate elliptic equations with lower order terms
David Cruz-Uribe, Scott Rodney
We prove a weak maximum principle for subsolutions of a degenerate, linear, second order elliptic operator with lower order terms, building on the existence results recently proved…
Bounded solutions of degenerate elliptic equations with an Orlicz-gain Sobolev inequality
David Cruz-Uribe, Sullivan F. MacDonald, Scott Rodney
We consider the boundedness and exponential integrability of solutions to the Dirichlet problem for the degenerate elliptic equation \[ -v^{-1}\mathrm{Div}(|\sqrt{Q}\nabla u|^{p-2}…
Existence and uniqueness of solutions of degenerate elliptic equations with lower order terms
Seyma Cetin, David Cruz-Uribe, Feyza Elif Dal +2
We prove the existence and uniqueness of solutions to a Dirichlet problem \[ \begin{cases} Lu = f + v^{-1}\text{Div}(v{\bf e} h), & x \in Ω; u = 0, & x \in \partial Ω, \end{cases…