Equivalence Between Uniform Lp∗ A Priori Bounds and Uniform L∞ A Priori Bounds for Subcritical p-Laplacian Equations
Mediterranean Journal Of Mathematics
We establish sufficient conditions for a uniform Lp⋆(Ω) bound to imply a uniform L∞(Ω) bound for positive weak solutions of subcritical p-Laplacian equations. We also provide an equivalent result for sequences of boundary-value problems. As consequences, we prove that any set of solutions with finite energy is L∞(Ω) a priori bounded, and also obtain an alternative proof of the existence of a priori bounds for subcritical power like nonlinearities.
A priori estimates, p-Laplacian equation, positive solutions, subcritical nonlinearity, gradient regularity
Nsoki Mavinga and R. Pardo.
"Equivalence Between Uniform Lp∗ A Priori Bounds and Uniform L∞ A Priori Bounds for Subcritical p-Laplacian Equations".
Mediterranean Journal Of Mathematics.