The Iterated Equation of 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...

On Axially Symmetric Solutions in the Electroweak Theory

We present the general ansatz, the energy density and the Chern-Simons charge for static axially symmetric configurations in the bosonic sector of the electroweak theory. Containing the sphaleron, the multisphalerons and the sphaleronantisphaleron pair at finite mixing angle, the ansatz further allows the construction of the sphaleron and multisphaleron barriers and of the bisphalerons at finit...