Classification of solutions to a biharmonic equation on the half-space and ball with pairs of conformal boundary operators
arxiv(2024)
Abstract
We introduce the notion of a biharmonic Poisson kernel associated with
certain pair of conformal boundary operators and present its explicit formula.
With this powerful tool, we next establish the classification theorems of
nonnegative solutions to a biharmonic equation on the upper half-space and unit
ball with proper pairs of conformal boundary operators.
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