scholarly journals Optimal partial regularity of second order parabolic systems under controllable growth condition

2014 ◽  
Vol 266 (8) ◽  
pp. 4908-4937 ◽  
Author(s):  
Shuhong Chen ◽  
Zhong Tan
Keyword(s):  
Growth Condition ◽  
Partial Regularity ◽  
Parabolic Systems ◽  
Second Order ◽  
Controllable Growth Condition ◽  
Controllable Growth ◽  
Optimal Partial Regularity

scholarly journals Partial regularity up to the boundary for solutions of subquadratic elliptic systems

2018 ◽  
Vol 7 (4) ◽  
pp. 469-483 ◽  
Author(s):  
Zhong Tan ◽  
Yanzhen Wang ◽  
Shuhong Chen
Keyword(s):  
Partial Regularity ◽  
Direct Method ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Singular Set ◽  
Nonlinear Elliptic Systems ◽  
Hölder Continuous ◽  
Nonlinear Elliptic ◽  
Controllable Growth Condition ◽  
Controllable Growth

AbstractIn this paper, we are concerned with the nonlinear elliptic systems in divergence form under controllable growth condition. We prove that the weak solution u is locally Hölder continuous besides a singular set by using the direct method and classical Morrey-type estimates. Here the Hausdorff dimension of the singular set is less than {n-p}. This result not only holds in the interior, but also holds up to the boundary.

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