Extremals for a weighted Morrey's inequality and a weighted $ p $-Laplace equation

Yubo Ni; Yubo Ni

doi:10.3934/math.2025183

AIMS Mathematics

2025, Volume 10, Issue 2: 3930-3944. doi: 10.3934/math.2025183

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Research article

Extremals for a weighted Morrey's inequality and a weighted $ p $-Laplace equation

Yubo Ni ^,

School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, Shaanxi, China

Received: 11 November 2024 Revised: 17 February 2025 Accepted: 18 February 2025 Published: 26 February 2025
MSC : 35A15, 35A23

We establish a weighted Morrey's inequality. Furthermore, the existence of extremals for this weighted Morrey's inequality is studied. As an application, we prove that extremals are the weak solutions of a related weighted $ p $-Laplace equation.
- weighted Morrey's inequality,
- extremal functions,
- $ p $-Laplace operator
Citation: Yubo Ni. Extremals for a weighted Morrey's inequality and a weighted $ p $-Laplace equation[J]. AIMS Mathematics, 2025, 10(2): 3930-3944. doi: 10.3934/math.2025183

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Abstract

We establish a weighted Morrey's inequality. Furthermore, the existence of extremals for this weighted Morrey's inequality is studied. As an application, we prove that extremals are the weak solutions of a related weighted $ p $-Laplace equation.

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