scholarly journals Some Remarks on Axially-Symmetric Potential Theory

1966 ◽  
Vol 16 (3) ◽  
pp. 203-212
Author(s):  
Albert Heins
Keyword(s):  
Potential Theory ◽  
Axially Symmetric ◽  
Symmetric Potential

Elliptic transmutation I

1982 ◽  
Vol 91 (3-4) ◽  
pp. 315-334 ◽  
Author(s):  
Robert Carroll
Keyword(s):  
Potential Theory ◽  
Elliptic Equations ◽  
Axially Symmetric ◽  
Hilbert Transforms ◽  
Symmetric Potential ◽  
First Case

SynopsisGiven and similar , modelled on radial Laplace-Beltrami operators (ρp = , in this paper we begin the study of transmutations which leads to elliptic equations Working with and transmutations Qm → −D2 for m > −½ and −D2 → for m < −½, we obtain a transmutation formulation and derivation of many results of generalized axially symmetric potential theory in the first case and in both cases generalized Hilbert transforms (different). Canonical generalizations are then automatic using general transmutation theory.

scholarly journals The iterated equation of generalized axially symmetric potential theory, VI General solutions

1974 ◽  
Vol 18 (3) ◽  
pp. 318-327
Author(s):  
J. C. Burns
Keyword(s):  
Potential Theory ◽  
Polar Coordinates ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
General Solutions ◽  
Real Value ◽  
Image Position

The iterated equation of generalized axially symmetric potential theory [1] is the equation where, in its simplest form, the operator Lk is defined by the function f f(x, y) being assumed to belong to the class of C2n functions and the parameter l to take any real value. In appropriate circumstances, which will be indicated later, the operator can be generalized but as this can be done without altering the methods used, the operator will be taken in the form where r, θ are polar coordinates such that x = r cos θ, y = r sin μ = cosθ.

scholarly journals Derivative-type ascent formulas for kernels of some half-space Dirichlet problems

2000 ◽  
Vol 42 (2) ◽  
pp. 185-194
Author(s):  
L. R. Bragg
Keyword(s):  
Potential Theory ◽  
Half Space ◽  
Laplace Equation ◽  
Bessel Functions ◽  
Axially Symmetric ◽  
Dirichlet Problems ◽  
Symmetric Potential ◽  
Derivative Type ◽  
Differentiation Formulas

AbstractDerivative-type ascent formulas are deduced for the kernels of certain half-space Dirichlet problems. These have the character of differentiation formulas for the Bessel functions but involve modifying variables after completing the differentiations. The Laplace equation and the equation of generalized axially-symmetric potential theory (GASPT) are considered in these. The methods employed also permit treating abstract versions of Dirichlet problems.

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