On regularity properties of a surface growth model

被引：5

作者：

Burczak, Jan ^{[1
,2
]}

Ozanski, Wojciech S. ^{[3
]}

Seregin, Gregory ^{[4
,5
]}

机构：

[1] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00656 Warsaw, Poland

[2] Univ Leipzig, Math Inst, Augustuspl 10, D-04109 Leipzig, Germany

[3] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA

[4] Univ Oxford, Oxford, England

[5] RAS, Steklov Math Inst, St Petersburg Dept, St Petersburg, Russia

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2021年 / 151卷 / 06期

基金：

欧洲研究理事会;

关键词：

Surface growth model; partial regularity; local higher integrability; singular set; box-counting dimension; Hausdorff dimension; THIN-FILM-GROWTH; WEAK SOLUTIONS;

D O I：

10.1017/prm.2020.84

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local smoothness of solutions.

引用

页码：1869 / 1892

页数：24

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