Well-posedness of degenerate differential equations in Hölder continuous function spaces

2014 ◽  
Vol 10 (2) ◽  
pp. 239-248 ◽  
Author(s):  
Shangquan Bu
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Function Spaces ◽  
Well Posedness ◽  
Hölder Continuous ◽  
Degenerate Differential Equations

Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces

2018 ◽  
Vol 62 (4) ◽  
pp. 715-726
Author(s):  
Shangquan Bu ◽  
Gang Cai
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Function Spaces ◽  
Linear Operators ◽  
Well Posedness ◽  
Third Order ◽  
Hölder Continuous ◽  
Vector Valued ◽  
Closed Linear Operators

AbstractIn this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$-Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$-well-posedness for the third order differential equations $au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$, ($t\in \mathbb{R}$), where $A,B$ are closed linear operators on a Banach space $X$ such that $D(A)\subset D(B)$, $a\in \mathbb{C}$ and $0<\unicode[STIX]{x1D6FC}<1$.

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.

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