Global integral gradient bounds for quasilinear equations below or near the natural exponent

Nguyen Cong Phuc Department of Mathematics, Louisiana State University

Analysis of PDEs mathscidoc:1701.03028

Arkiv for Matematik, 52, (2), 329-354, 2012.6
We obtain sharp integral potential bounds for gradients of solutions to a wide class of quasilinear elliptic equations with measure data. Our estimates are global over bounded domains that satisfy a mild exterior capacitary density condition. They are obtained in Lorentz spaces whose degrees of integrability lie below or near the natural exponent of the operator involved. As a consequence, nonlinear Calderón–Zygmund type estimates below the natural exponent are also obtained for $\mathcal{A}$ -superharmonic functions in the whole space ℝ^{$n$}. This answers a question raised in our earlier work (On Calderón–Zygmund theory for$p$- and $\mathcal{A}$ -superharmonic functions, to appear in$Calc. Var. Partial Differential Equations$, DOI10.1007/s00526-011-0478-8) and thus greatly improves the result there.
No keywords uploaded!
[ Download ] [ 2017-01-08 20:36:37 uploaded by arkivadmin ] [ 81 downloads ] [ 0 comments ] [ Cited by 6 ]
@inproceedings{nguyen2012global,
  title={Global integral gradient bounds for quasilinear equations below or near the natural exponent},
  author={Nguyen Cong Phuc},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637628084061},
  booktitle={Arkiv for Matematik},
  volume={52},
  number={2},
  pages={329-354},
  year={2012},
}
Nguyen Cong Phuc. Global integral gradient bounds for quasilinear equations below or near the natural exponent. 2012. Vol. 52. In Arkiv for Matematik. pp.329-354. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637628084061.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved