Topological Methods In Nonlinear Analysis
We provide sufficient conditions for a uniform L²⋆(Ω) bound to imply a uniform L∞(Ω) bound for positive classical solutions to a class of subcritical elliptic problems in bounded C² domains in Rᴺ. We also establish an equivalent result for sequences of boundary value problems.
A. Castro, Nsoki Mavinga, and R. Pardo.
"Equivalence Between Uniform L²⋆(Ω) A-Priori Bounds And Uniform L∞(Ω) A-Priori Bounds For Subcritical Elliptic Equations".
Topological Methods In Nonlinear Analysis.