Equivalence Between Uniform Lp∗ A Priori Bounds and Uniform L∞ A Priori Bounds for Subcritical p-Laplacian Equations
Document Type
Article
Publication Date
2021
Published In
Mediterranean Journal Of Mathematics
Abstract
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.
Keywords
A priori estimates, p-Laplacian equation, positive solutions, subcritical nonlinearity, gradient regularity
Recommended Citation
Nsoki Mavinga and R. Pardo.
(2021).
"Equivalence Between Uniform Lp∗ A Priori Bounds and Uniform L∞ A Priori Bounds for Subcritical p-Laplacian Equations".
Mediterranean Journal Of Mathematics.
Volume 18,
DOI: 10.1007/s00009-020-01673-6
https://works.swarthmore.edu/fac-math-stat/261