Gradient estimates for solutions of elliptic systems with measurable coefficients from composite material

2018 ◽  
Vol 41 (16) ◽  
pp. 7007-7031
Author(s):  
Yunsoo Jang ◽  
Youchan Kim
Keyword(s):  
Composite Material ◽  
Elliptic Systems ◽  
Gradient Estimates ◽  
Measurable Coefficients

scholarly journals Gradient estimates for semilinear elliptic systems and other related results

2015 ◽  
Vol 145 (6) ◽  
pp. 1313-1330 ◽  
Author(s):  
Panayotis Smyrnelis
Keyword(s):  
Liouville Theorem ◽  
Elliptic Systems ◽  
Gradient Estimates ◽  
Alternative Form ◽  
Strong Monotonicity ◽  
Energy Tensor ◽  
Planar Domains ◽  
Stress Energy ◽  
General Phase ◽  
Double Well Potential

A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville theorem for general phase transition potentials. Gradient estimates are also established for several kinds of elliptic systems. They allow us to prove the Liouville theorem in some particular cases. Finally, we give an alternative form of the stress–energy tensor for solutions defined in planar domains. As an application, we deduce a (strong) monotonicity formula.

Gradient estimates for elliptic systems in non-smooth domains

2008 ◽  
Vol 341 (3) ◽  
pp. 629-650 ◽  
Author(s):  
Sun-Sig Byun ◽  
Lihe Wang
Keyword(s):  
Elliptic Systems ◽  
Gradient Estimates
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