scholarly journals $ W^{1,p} $ estimates for elliptic systems on composite material with almost partially BMO coefficients

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Caiyan Li ◽  
Dongsheng Li
Keyword(s):  
Composite Material ◽  
Elliptic Systems ◽  
Bmo Coefficients

scholarly journals Second Order Regularity for a Linear Elliptic System Having BMO Coefficients

2021 ◽  
Author(s):  
Gioconda Moscariello ◽  
Giulio Pascale
Keyword(s):  
Dirichlet Problem ◽  
Unit Ball ◽  
Elliptic System ◽  
Positive Constant ◽  
Elliptic Systems ◽  
Second Order ◽  
Identity Matrix ◽  
Bmo Coefficients

AbstractWe consider linear elliptic systems whose prototype is $$\begin{aligned} div \, \Lambda \left[ \,\exp (-|x|) - \log |x|\,\right] I \, Du = div \, F + g \text { in}\, B. \end{aligned}$$ d i v Λ exp ( - | x | ) - log | x | I D u = d i v F + g in B . Here B denotes the unit ball of $$\mathbb {R}^n$$ R n , for $$n > 2$$ n > 2 , centered in the origin, I is the identity matrix, F is a matrix in $$W^{1, 2}(B, \mathbb {R}^{n \times n})$$ W 1 , 2 ( B , R n × n ) , g is a vector in $$L^2(B, \mathbb {R}^n)$$ L 2 ( B , R n ) and $$\Lambda $$ Λ is a positive constant. Our result reads that the gradient of the solution $$u \in W_0^{1, 2}(B, \mathbb {R}^n)$$ u ∈ W 0 1 , 2 ( B , R n ) to Dirichlet problem for system (0.1) is weakly differentiable provided the constant $$\Lambda $$ Λ is not large enough.

Estimates for elliptic systems from composite material

2003 ◽  
Vol 56 (7) ◽  
pp. 892-925 ◽  
Author(s):  
YanYan Li ◽  
Louis Nirenberg
Keyword(s):  
Composite Material ◽  
Elliptic Systems

Atomic structure of interface of intermetallic compound TiAl and nitride Ti2AIN using HREM and image processing

1991 ◽  
Vol 49 ◽  
pp. 570-571
Author(s):  
E. Sukedai ◽  
H. Mabuchi ◽  
H. Hashimoto ◽  
Y. Nakayama
Keyword(s):  
Mechanical Properties ◽  
Image Processing ◽  
Composite Material ◽  
Intermetallic Compound ◽  
Side Surface ◽  
High Resolution Electron Microscopy ◽  
Hexagonal Structure ◽  
Second Phase ◽  
Resolution Electron ◽  
Compound Tial

In order to improve the mechanical properties of an intermetal1ic compound TiAl, a composite material of TiAl involving a second phase Ti2AIN was prepared by a new combustion reaction method. It is found that Ti2AIN (hexagonal structure) is a rod shape as shown in Fig.1 and its side surface is almost parallel to the basal plane, and this composite material has distinguished strength at elevated temperature and considerable toughness at room temperature comparing with TiAl single phase material. Since the property of the interface of composite materials has strong influences to their mechanical properties, the structure of the interface of intermetallic compound and nitride on the areas corresponding to 2, 3 and 4 as shown in Fig.1 was investigated using high resolution electron microscopy and image processing.

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