Weighted Function Spaces on Domains and Degenerate Elliptic Differential Equations

1983 ◽  
pp. 260-263
Author(s):  
Hans Triebel
Keyword(s):  
Differential Equations ◽  
Function Spaces ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Elliptic Differential Equations ◽  
Degenerate Elliptic

scholarly journals Hölder continuity of solutions of some degenerate elliptic differential equations

2000 ◽  
Vol 62 (3) ◽  
pp. 369-377 ◽  
Author(s):  
Ahmed Mohammed
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Weak Solutions ◽  
Function Spaces ◽  
Elliptic Differential Equation ◽  
Holder Continuity ◽  
Hölder Continuous ◽  
Elliptic Differential Equations ◽  
Continuity Of Solutions ◽  
Degenerate Elliptic

Weak solutions of the degenerate elliptic differential equation Lu := −div(A (x)∇u)+b·∇u+Vu = f, with |b|2ω−1, V, f in some appropriate function spaces, will be shown to be Hölder continuous.

scholarly journals Linear Differential Equations on Some Classes of Weighted Function Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1113
Author(s):  
Ahmed El-Sayed Ahmed ◽  
Amnah E. Shammaky
Keyword(s):  
Specific Growth ◽  
Function Spaces ◽  
Entire Solutions ◽  
Linear Type ◽  
Weighted Function ◽  
Weighted Function Spaces ◽  
Type Classes ◽  
Type Differential Equation ◽  
Linear Differential ◽  
Weighted Type

Some weighted-type classes of holomorphic function spaces were introduced in the current study. Moreover, as an application of the new defined classes, the specific growth of certain entire-solutions of a linear-type differential equation by the use of concerned coefficients of certain analytic-type functions, that is the equation h(k)+Kk−1(υ)h(k−1)+…+K1(υ)h′+K0(υ)h=0, will be discussed in this current research, whereas the considered coefficients K0(υ),…,Kk−1(υ) are holomorphic in the disc ΓR={υ∈C:|υ|<R},0<R≤∞. In addition, some non-trivial specific examples are illustrated to clear the roles of the obtained results with some sharpness sense. Hence, the obtained results are strengthen to some previous interesting results from the literature.

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