Strict Monotonicity and Unique Continuation for the Third-Order Spectrum of Biharmonic Operator

Abstract EN

We will study the spectrum for the biharmonic operator involving the laplacian and the gradient of the laplacian with weight, which we call third-order spectrum.

We will show that the strict monotonicity of the eigenvalues of the operator Δ2u+2β·∇(Δu)+|β|2Δu, where β∈ℝN, holds if some unique continuation property is satisfied by the corresponding eigenfunctions.