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

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).

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• Doubling Inequality at the Boundary for the Kirchhoff -- Love Plate's Equation with Dirichlet Conditions