scholarly journals Partial regularity for subquadratic parabolic systems under controllable growth conditions

2016 ◽  
Vol 439 (2) ◽  
pp. 481-513 ◽  
Author(s):  
Yichen Dai ◽  
Zhong Tan ◽  
Shuhong Chen
Keyword(s):  
Partial Regularity ◽  
Parabolic Systems ◽  
Growth Conditions ◽  
Controllable Growth

scholarly journals Partial Regularity for Nonlinear Subelliptic Systems with Dini Continuous Coefficients in Heisenberg Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Jialin Wang ◽  
Pingzhou Hong ◽  
Dongni Liao ◽  
Zefeng Yu
Keyword(s):  
Weak Solution ◽  
Heisenberg Group ◽  
Partial Regularity ◽  
Harmonic Approximation ◽  
Growth Conditions ◽  
Heisenberg Groups ◽  
Hölder Exponent ◽  
Hölder Continuous ◽  
Horizontal Gradients ◽  
Controllable Growth

This paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg groupℍn. Based on a generalization of the technique of𝒜-harmonic approximation introduced by Duzaar and Steffen, partial regularity to the sub-elliptic system is established in the Heisenberg group. Our result is optimal in the sense that in the case of Hölder continuous coefficients we establish the optimal Hölder exponent for the horizontal gradients of the weak solution on its regular set.

scholarly journals Variational inequalities for energy functionals with nonstandard growth conditions

1998 ◽  
Vol 3 (1-2) ◽  
pp. 41-64 ◽  
Author(s):  
Martin Fuchs ◽  
Li Gongbao
Keyword(s):  
Variational Inequalities ◽  
Obstacle Problem ◽  
Partial Regularity ◽  
Growth Conditions ◽  
Energy Functionals ◽  
Nonstandard Growth ◽  
Bounded Lipschitz Domain ◽  
Growth Properties ◽  
Nonstandard Growth Conditions ◽  
Special Case

We consider the obstacle problem{minimize????????I(u)=?OG(?u)dx??among functions??u:O?Rsuch?that???????u|?O=0??and??u=F??a.e.for a given functionF?C2(O¯),F|?O<0and a bounded Lipschitz domainOinRn. The growth properties of the convex integrandGare described in terms of aN-functionA:[0,8)?[0,8)withlimt?8¯A(t)t-2<8. Ifn=3, we prove, under certain assumptions onG,C1,8-partial regularity for the solution to the above obstacle problem. For the special case whereA(t)=tln(1+t)we obtainC1,a-partial regularity whenn=4. One of the main features of the paper is that we do not require any power growth ofG.

Partial regularity for quasilinear nonuniformly parabolic systems

1998 ◽  
Vol 92 (6) ◽  
pp. 4286-4301
Author(s):  
A. V. Ivanov ◽  
N. Kikuchi ◽  
M. Fraska
Keyword(s):  
Partial Regularity ◽  
Parabolic Systems
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