On Green's functions in generalized axially symmetric potential theory

ABSTRACT

Fundamental solutions and Green's functions of the operator ${\mathrm{\partial }}_t^2+(1+2\alpha )t^{-1}{\mathrm{\partial }}_t+{\mathrm{\Delta }}_n,$ $\alpha \in \mathbb{C},$ are calculated in the half-space $t>0.$

KEYWORDS:

• Fundamental solutions
• generalized axially symmetric potential theory
• Dirichlet problem
• Neumann problem
• Green's function

AMS SUBJECT CLASSIFICATIONS:

• 35A08
• 35J70
• 35A22
• 46F12

Disclosure statement

No potential conflict of interest was reported by the authors.