Title

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

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