2020/04/14 by Thanh‐Nhan Nguyen, Nguyen, Thanh-Nhan, Minh‐Phuong Tran +1 · 1 citation
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2004.06394
openalex publication_date 2020/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to establish an abstract theory based on the\nso-called fractional-maximal distribution functions (FMDs). From the rough\nideas introduced in~ citeAM2007, we develop and prove some abstract results\nrelated to the level-set inequalities and norm-comparisons by using the\nlanguage of such FMDs. Particularly interesting is the applicability of our\napproach that has been shown in regularity and Calder 'on-Zygmund type\nestimates. In this paper, due to our research experience, we will establish\nglobal regularity estimates for two types of general quasilinear problems\n(problems with divergence form and double obstacles), via fractional-maximal\noperators and FMDs. The range of applications of these abstract results is\nlarge. Apart from these two examples of the regularity theory for elliptic\nequations discussed, it is also promising to indicate further possible\napplications of our approach for other special topics.\n