Equivalence between uniform Lp∗ a priori bounds and uniform L∞ a priori bounds for subcritical p-laplacian equations

Mavinga, NsokiPardo San Gil, Rosa María2024-05-222024-05-222021-01-04Mavinga, N., Pardo, R. Equivalence between uniform a priori bounds and uniform a priori bounds for subcritical p-laplacian equations. Mediterr. J. Math. 18, 13 (2021). https://doi.org/10.1007/s00009-020-01673-610.1007/s00009-020-01673-6 1660-5446/21/010001-24https://hdl.handle.net/20.500.14352/104327We establish sufficient conditions for a uniform Lp⋆ (Ω) bound to imply a uniform L∞(Ω) bound for positive weak solutions of sub- critical 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Equivalence between uniform Lp∗ a priori bounds and uniform L∞ a priori bounds for subcritical p-laplacian equationsjournal articlehttps://doi.org/10.1007/s00009-020-01673-6https://link.springer.com/article/10.1007/s00009-020-01673-6restricted access51A priori estimatesp-Laplacian equationPositive solutionsSubcritical nonlinearityGradient regularityCiencias12 Matemáticas