A SHORT PROOF FOR LEVEL-SET INEQUALITIES ON DISTRIBUTION FUNCTIONS
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Abstract
The regularity of solutions to quasi-linear elliptic equations is one of the most interesting topics of research for many mathematicians with different methods. A new method has been established to study this problem, via level-set inequalities on fractional maximal distribution functions. This method is very efficient and able to apply to many classes of partial differential equations. The sufficient conditions to build the level-set inequalities are key to obtain the Lorentz estimates in this method. In this article, we give a short proof for the level-set inequalities on fractional maximal distribution functions, which is based on one sufficient condition instead of two in a paper by Nguyen and Tran (2021a).
Keywords
gradient estimates, level-set inequalities on distribution functions, Lorentz spaces, p-Laplace equations
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References
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