We prove a three spheres 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 flattened 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 a bi-Laplacian principal part.

Optimal Three Spheres Inequality at the Boundary for the Kirchhoff–Love Plate’s Equation with Dirichlet Conditions

Alessandrini, Giovanni;Rosset, Edi;
2019-01-01

Abstract

We prove a three spheres 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 flattened 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 a bi-Laplacian principal part.
2019
27-ago-2018
Pubblicato
https://link.springer.com/article/10.1007/s00205-018-1302-9
https://arxiv.org/pdf/1802.08631.pdf
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2931406
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