The aim of this short paper is to show that some assumptions in Guarnotta et al. (Adv Nonlinear Anal 11:741--756, 2022) can be relaxed and even dropped when looking for weak solutions instead of strong ones. This improvement is a consequence of two results concerning gradient terms: an $L^\infty$ estimate, which exploits nonlinear potential theory, and a compactness result, based on the classical Riesz-Fréchet-Kolmogorov theorem.
A note on gradient estimates for p-Laplacian equations
Guarnotta, Umberto
;Marano, Salvatore A.
2023-01-01
Abstract
The aim of this short paper is to show that some assumptions in Guarnotta et al. (Adv Nonlinear Anal 11:741--756, 2022) can be relaxed and even dropped when looking for weak solutions instead of strong ones. This improvement is a consequence of two results concerning gradient terms: an $L^\infty$ estimate, which exploits nonlinear potential theory, and a compactness result, based on the classical Riesz-Fréchet-Kolmogorov theorem.File in questo prodotto:
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