Solvability of boundary problems for general elliptic systems

1968 ◽  
pp. 182-225 ◽  
Author(s):  
L. R. Volevič
Keyword(s):  
Elliptic Systems ◽  
Boundary Problems ◽  
General Elliptic

Liouville theorems for linear elliptic systems

1983 ◽  
Vol 94 (3-4) ◽  
pp. 309-322 ◽  
Author(s):  
N. Weck
Keyword(s):  
Elliptic Systems ◽  
Elliptic Pde ◽  
Liouville Theorems ◽  
General Elliptic ◽  
Pde Systems ◽  
Coerciveness Estimate

SynopsisLiouville theorems are obtained for general elliptic PDE-systems ℒU(x): = Σlɑl≦21Aα(x) əαU(x)=0 essentially under the assumption that ℒ satisfies a coerciveness estimate over .

Green matrices and continuity of the weak solutions for the elliptic systems with lower order terms

2016 ◽  
Vol 27 (02) ◽  
pp. 1650010
Author(s):  
Jinping Zhuge ◽  
Zhenqiu Zhang
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Lower Order ◽  
Elliptic Systems ◽  
Pointwise Estimates ◽  
Schauder Estimates ◽  
General Elliptic ◽  
Method Of Potentials ◽  
Type Classes ◽  
Lower Order Terms

In this paper, we consider the second-order elliptic systems with lower order terms coefficients belonging to Kato–Stummel type classes in a bounded domain [Formula: see text], where [Formula: see text]. We establish the existence, global pointwise estimates and [Formula: see text] estimates for Green matrices. Based on these estimates, we are able to show the continuity of weak solutions for the general elliptic systems by using method of potentials. We also obtain the optimal Schauder estimates for weak solutions.

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