Polyharmonic polynomials and mixed boundary value problems in the Heisenberg group $\mathbb H_n$
S. Dubey, A. Kumar, M. M. Mishra
TL;DR
This paper investigates polyharmonic boundary value problems in the Heisenberg group, providing solvability conditions for Neumann and mixed boundary problems on the Korányi ball, advancing understanding of sub-Riemannian PDEs.
Contribution
It establishes necessary and sufficient conditions for solvability of polyharmonic boundary value problems in the Heisenberg group, a novel contribution to sub-Riemannian analysis.
Findings
Derived solvability conditions for Neumann problems
Established criteria for mixed boundary value problems
Enhanced understanding of polyharmonic equations in Heisenberg group
Abstract
We study the polyharmonic Neumann and mixed boundary value problems on the Kor\'{a}nyi 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.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Holomorphic and Operator Theory · Spectral Theory in Mathematical Physics