arXiv subjects
Publications and source records attributed to M. M. Mishra.
We study the polyharmonic Neumann and mixed boundary value problems on the Korányi ball in the Heisenberg group $\H_n$. Necessary and sufficient solvability conditions are obtained for the nonhomogeneous polyharmonic Neumann problem and Neumann-Dirichlet boundary value problems.
Existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian on the Korányi ball of the Heisenberg group $\mathbb{H}_n$ are discussed. Explicit representations of Green's type function (Neumann function) for the half space and Korányi ball in $\mathbb{H}_n$ for circular functions have been obtained. These functions are then used on above regions in $\mathbb{H}_n$ to solve the inhomogeneous Neumann boundary value problem for circular data.