Poisson's equation and generalized axially symmetric potential theory

Generalized Axially Symmetric Potential Theory

A double layer potentials for generalized bi-axially symmetric equation

were constructed in R 2 = {(x, y) : x > 0, y > 0} . In the present paper (in case of λ = 0) using the constructed fundamental solutions, a double layer potentials are defined and investigated. Limiting theorems are proved, and integral equations concerning a denseness of potentials of a double layer are found. MSC: Primary 35J15, 35J70.

The Dirichlet Problem for the Generalized Bi-axially Symmetric Helmholtz Equation

Abstract. In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in R 2 = {(x, y) : x > 0, y > 0} . They contain Kummer’s confluent hypergeometric functions in three variables. In this paper, using one of the constructed fundamental solutions, the Dirichlet problem is solved in the domain Ω ⊂ R 2 . Using the method of Green’s functions, solut...

On the Domain of Regularity of Generalized Axially Symmetric Potentials

which depends analytically on the two real variables x and y in a domain containing a segment of the singular line y — 0, is uniquely determined by its values on y = 0. In this note we shall consider the following problem: If the function g(z) =u(z, 0) is continued to complex values of z, to what extent does its domain of regularity determine the domain of regularity of u(x, y)? A partial answe...

Quasi-axially symmetric stellarators.

Confinement of a plasma for controlled thermonuclear fusion is studied numerically. Toroidal equilibria are considered, with an emphasis on the Modular Helias-like Heliac 2 (MHH2), which is a stellarator of low aspect ratio with just two field periods surrounded by 16 modular coils. The geometry is fully three-dimensional, but there is an axial symmetry of the magnetic structure that is calcula...