Precise estimates for the fundamental solutions to some degenerate elliptic differential equations

1986 ◽  
pp. 129-133
Author(s):  
Shigeo Kusuoka
Keyword(s):  
Differential Equations ◽  
Fundamental Solutions ◽  
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 Weak solutions of a quasi-linear degenerate elliptic system with discontinuous coefficients

1984 ◽  
Vol 94 ◽  
pp. 105-135
Author(s):  
Yoshiaki Ikeda
Keyword(s):  
Differential Equations ◽  
Elliptic System ◽  
Bounded Domain ◽  
Weak Solutions ◽  
Discontinuous Coefficients ◽  
Degenerate Elliptic System ◽  
Elliptic Differential Equations ◽  
Degenerate Elliptic ◽  
Linear Degenerate

We shall discuss regularities and related topics on weak solutions of the system of the following quasi-linear elliptic differential equations (a combination of almost single equations)in a bounded domain Ω in Rn (n ≧ 2), where A1j … (A1j …, Anj) are given vector functions of (x, u, ▽uj), Bj are scalar functions of the same variables, and ▽uj = (∂uj/∂x1, …, ∂uj/∂xj denote the gradients of the uj = uj(x) (j = 1, …, m).

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