Pointwise potential estimates for solutions to a class of nonlinear elliptic equations with measure data

Zhaoyue Sui; Feng Zhou; Zhaoyue Sui; Feng Zhou

doi:10.3934/math.2025370

AIMS Mathematics

2025, Volume 10, Issue 4: 8066-8094. doi: 10.3934/math.2025370

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Research article

Pointwise potential estimates for solutions to a class of nonlinear elliptic equations with measure data

Zhaoyue Sui ,
Feng Zhou ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, 250358, China

Received: 17 January 2025 Revised: 19 March 2025 Accepted: 24 March 2025 Published: 07 April 2025
MSC : 35J60, 35R05, 35R06

In this article, we investigate the regularities of solutions to a class of nonlinear elliptic equations with measure data. These equations involve the $ N $-functions, and the solutions belong to the Sobolev-Orlicz spaces. Through the application of comparison arguments, Caccioppoli-type inequality, and maximal estimate, we derive pointwise Riesz potential estimates for both the gradient of the solutions and the solutions themselves. Furthermore, we establish Hölder continuity estimates for the solutions.
- Riesz potential,
- nonlinear elliptic equations,
- regularity,
- Sobolev-Orlicz spaces
Citation: Zhaoyue Sui, Feng Zhou. Pointwise potential estimates for solutions to a class of nonlinear elliptic equations with measure data[J]. AIMS Mathematics, 2025, 10(4): 8066-8094. doi: 10.3934/math.2025370

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Abstract

In this article, we investigate the regularities of solutions to a class of nonlinear elliptic equations with measure data. These equations involve the $ N $-functions, and the solutions belong to the Sobolev-Orlicz spaces. Through the application of comparison arguments, Caccioppoli-type inequality, and maximal estimate, we derive pointwise Riesz potential estimates for both the gradient of the solutions and the solutions themselves. Furthermore, we establish Hölder continuity estimates for the solutions.

References

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