4 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}…
Regularity of Singular Solutions to -Poisson Equations
Sullivan Francis MacDonald
This work showcases level set estimates for weak solutions to the -Poisson equation on a bounded domain, which we use to establish Lebesgue space inclusions for weak solutions.…
Bounded Weak Solutions of Degenerate -Poisson Equations
Sullivan Francis MacDonald, Scott Rodney
In this work we study global boundedness and exponential integrability of weak solutions to degenerate -Poisson equations using an iterative method of De Giorgi type. Given a sy…
Families of Young Functions and Limits of Orlicz Norms
Scott Rodney, Sullivan F. MacDonald
Given a -finite measure space , a Young function , and a one-parameter family of Young functions , we find necessary and sufficient conditions for the associa…