Doubling inequality at the boundary for the Kirchhoff-Love plate's equation with supported conditions

TL;DR

This paper establishes a boundary doubling inequality for solutions to the Kirchhoff-Love plate equation with supported boundary conditions, using conformal mapping, reflection, and Carleman inequalities, leading to a strong unique continuation property at the boundary.

Contribution

It introduces a novel boundary doubling inequality for the Kirchhoff-Love plate equation, combining conformal mapping, reflection, and Carleman inequalities to prove SUCPB.

Findings

Boundary doubling inequality at the boundary.

Strong Unique Continuation Property at the boundary.

Method combining conformal mapping, reflection, and Carleman inequalities.

Abstract

In this article we derive a doubling inequality at the boundary for solutions to the Kirchhoff-Love isotropic plate's equation satisfying supported boundary conditions. To this end, we combine the use of a suitable conformal mapping which flattens the boundary and a reflection argument which guarantees the needed regularity of the extended solution. We finally apply inequalities of Carleman type in order to derive the result. The latter implies Strong Unique Continuation Property at the boundary (SUCPB).