Regularity results for nonlinear parabolic obstacle problems with subquadratic growth

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Erhardt, Andre H.¹ 

[1] Univ Hohenheim, Inst Appl Math & Stat, Emil Wolff Str 27, D-70599 Stuttgart, Germany

关键词: Holder continuity;    Lipschitz continuity;    Nonlinear parabolic obstacle problems;    Variational inequality;    Localizable solution;    Irregular obstacles;   

DOI  :  10.1016/j.jde.2016.09.006

来源: Elsevier

【 摘 要 】

In [26] it was shown that the spatial gradient of the solution u to the parabolic obstacle problem with superquadratic growth is local Holder continuous provided the obstacle is regular enough. In this paper, we extend this regularity result to the subquadratic case. This means we establish the local Holder continuity of the spatial gradient of the solution u to the parabolic obstacle problem with subquadratic growth. More precisely, we prove that Du is an element of C-loc(0;alpha,alpha/2) for some alpha is an element of (0,1), provided the coefficients and the obstacle are regular enough. Moreover, we use the local Holder continuity to prove the local Lipschitz continuity of the solution u, i.e. u is an element of C-loc(0;1,1/2). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free