170 citations · 272 across the 45 of their papers we have counts for
12 papers · 1 filter
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}…
Bounded weak solutions with Orlicz space data: an overview
David Cruz-Uribe
It is well known that non-negative solutions to the Dirichlet problem in a bounded domain , where , , satisfy $\|u\|_{L^\infty(Ω)} \leq C\|f\|_…
Degenerate parabolic -Laplacian equations: existence, uniqueness and asymptotic behavior of solutions
David Cruz-Uribe, Kabe Moen, Yuanzhen Shao
In this paper we study the degenerate parabolic -Laplacian,, where the degeneracy is controlled by a mat…
Poincaré Inequalities and Neumann Problems for the Variable Exponent Setting
David Cruz-Uribe, Michael Penrod, Scott Rodney
We extend the results of [5], where we proved an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a family of Neumann problems related to a…
Bounded weak solutions to elliptic PDE with data in Orlicz spaces
David Cruz-Uribe, Scott Rodney
A classical regularity result is that non-negative solutions to the Dirichlet problem in a bounded domain , where , , satisfy $\|u\|_{L^\infty(…
Global Sobolev inequalities and Degenerate P-Laplacian equations
David Cruz-Uribe, Scott Rodney, Emily Rosta
We prove that a local, weak Sobolev inequality implies a global Sobolev estimate using existence and regularity results for a family of -Laplacian equations. Given $Ω\subset\mat…