Biharmonic Continuations of Gradients with the Help of Monogenic Functions with Values in the Biharmonic Algebra
摘要
Necessary and sufficient conditions are established for the existence of continuations of the gradients of biharmonic functions u1 and u2 across a smooth curve Γ (uk : Dk → ℝ, k = 1, 2, and Γ is a common part of the boundaries of D1 and D2). Moreover, the indicated continuations of gradients determine the gradient of the biharmonic function (in D1 ∪ Γ ∪ D1).