@article{Nguyen2023, 
author = {Quoc-Hung Nguyen and Nguyen Cong Phuc},
title = {Universal potential estimates for    1  <  p  ≤  2  −      1    n},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {3},
pages = {1-24},
keywords = {pointwise estimate, potential estimate, Wolff's potential, Riesz's potential, fractional maximal function, Calderón space, p-Laplacian, quasilinear equation, measure data},
url = {https://www.sciopen.com/article/10.3934/mine.2023057},
doi = {10.3934/mine.2023057},
abstract = {We extend the so-called universal potential estimates of Kuusi-Mingione type (J. Funct. Anal. 262: 4205–4269, 2012) to the singular case    1  <  p  ≤  2  −  1      /    n for the quasilinear equation with measure data     −  div  ⁡  (  A  (  x  ,  ∇  u  )  )  =  μin a bounded open subset    Ω of              R        n  ,    n  ≥  2, with a finite signed measure    μ in    Ω. The operator    div  ⁡  (  A  (  x  ,  ∇  u  )  ) is modeled after the    p-Laplacian        Δ    p    u  :=      d    i    v      (      |    ∇  u            |              p      −      2        ∇  u  ), where the nonlinearity    A  (  x  ,  ξ  ) (   x  ,  ξ  ∈            R        n  ) is assumed to satisfy natural growth and monotonicity conditions of order    p, as well as certain additional regularity conditions in the    x-variable.}
}