The method of p-harmonic approximation and optimal interior partial regularity for energy minimizing p-harmonic maps under the controllable growth condition

2007 ◽  
Vol 50 (1) ◽  
pp. 105-115 ◽  
Author(s):  
Shu-hong Chen ◽  
Zhong Tan
Keyword(s):  
Growth Condition ◽  
Partial Regularity ◽  
Harmonic Maps ◽  
Harmonic Approximation ◽  
Controllable Growth Condition ◽  
Controllable Growth

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.

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 Partial regularity of $p(x)$-harmonic maps

2012 ◽  
Vol 365 (6) ◽  
pp. 3329-3353 ◽  
Author(s):  
Maria Alessandra Ragusa ◽  
Atsushi Tachikawa ◽  
Hiroshi Takabayashi
Keyword(s):  
Partial Regularity ◽  
Harmonic Maps

A partial regularity theorem for harmonic maps at a free boundary

1989 ◽  
Vol 2 (4) ◽  
pp. 299-343 ◽  
Author(s):  
Frank Duzaar ◽  
Klaus Steffen
Keyword(s):  
Free Boundary ◽  
Partial Regularity ◽  
Harmonic Maps ◽  
Regularity Theorem
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