Logarithmic Convexity for Discrete Harmonic Functions and the Approximation of the Cauchy Problem for Poisson's Equation

1986 ◽  
Vol 47 (175) ◽  
pp. 135 ◽  
Author(s):  
R. S. Falk ◽  
P. B. Monk
Keyword(s):  
Cauchy Problem ◽  
Harmonic Functions ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Logarithmic Convexity ◽  
The Cauchy Problem ◽  
Discrete Harmonic Functions

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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