Optimal three spheres inequality at the boundary for the Kirchhoff-Love plate's equation with Dirichlet conditions

Abstract

We prove a three sphere inequality with optimal exponent at the boundary for solutions to the Kirchhoff-Love plate's equation satisfying homogeneous Dirichlet conditions. This result implies the Strong Unique Continuation Property at the Boundary (SUCPB). Our approach is based on the method of Carleman estimates, and involves the construction of an ad hoc conformal mapping preserving the structure of the operator and the employment of a suitable reflection of the solution with respect to the flatten boundary which ensures the needed regularity of the extended solution. To the authors' knowledge, this is the first (nontrivial) SUCPB result for fourth-order equations with bi-Laplacian principal part.

arXiv comment36 pages, to appear on Archive for Rational Mechanics and Analysis

References in corpus (4)

• The stability for the Cauchy problem for elliptic equations
• Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates
• Spectral inequality and resolvent estimate for the bi-Laplace operator
• On the dependence of the reflection operator on boundary conditions for biharmonic functions

Cited by in corpus (5)

• Stable determination of a rigid scatterer in elastodynamics
• Doubling inequality at the boundary for the Kirchhoff-Love plate's equation with supported conditions
• Inverse Problem for Kirchhoff-Love Plate Equation
• Unique continuation for a non bi-Laplacian fourth order elliptic operator
• Optimal stability in the identification of a rigid inclusion in an isotropic Kirchhoff-Love plate