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math.AP2024
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}…
math.AP2023
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.…