scholarly journals Pointwise gradient estimates for subquadratic elliptic systems with discontinuous coefficients

2019 ◽  
Vol 18 (6) ◽  
pp. 3137-3160
Author(s):  
Feng Zhou ◽  
◽  
Zhenqiu Zhang ◽  
Keyword(s):  
Elliptic Systems ◽  
Discontinuous Coefficients ◽  
Gradient Estimates

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.

Computational investigation of elliptic systems with discontinuous coefficients

2000 ◽  
Vol 36 (4) ◽  
pp. 605-609
Author(s):  
V. V. Skopetskii ◽  
S. I. Lyashko ◽  
S. A. Voitsekhovskiib
Keyword(s):  
Elliptic Systems ◽  
Discontinuous Coefficients ◽  
Computational Investigation

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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