The main result of this paper is a doubling inequality at the boundary for solutions to the Kirchhoff-Love isotropic plate's equation satisfying homogeneous Dirichlet conditions. This result, like the three sphere inequality with optimal exponent at the boundary proved in Alessandrini, Rosset, Vessella, Arch. Ration. Mech. Anal. (2019), implies the Strong Unique Continuation Property at the Boundary (SUCPB). Our approach is based on a suitable Carleman estimate, and involves an ad hoc reflection of the solution. We also give a simple application of our main result, by weakening the standard hypotheses ensuring uniqueness for the Cauchy problem for the plate equation.

DOUBLING INEQUALITY AT THE BOUNDARY FOR THE KIRCHHOFF-LOVE PLATE'S EQUATION WITH DIRICHLET CONDITIONS / Morassi, Antonino ; Rosset, Edi ; Vessella, Sergio. - In: LE MATEMATICHE. - ISSN 0373-3505. - STAMPA. - 75:(2020), pp. 27-55. [10.4418/2020.75.1.2]

DOUBLING INEQUALITY AT THE BOUNDARY FOR THE KIRCHHOFF-LOVE PLATE'S EQUATION WITH DIRICHLET CONDITIONS

Vessella, Sergio
2020

Abstract

The main result of this paper is a doubling inequality at the boundary for solutions to the Kirchhoff-Love isotropic plate's equation satisfying homogeneous Dirichlet conditions. This result, like the three sphere inequality with optimal exponent at the boundary proved in Alessandrini, Rosset, Vessella, Arch. Ration. Mech. Anal. (2019), implies the Strong Unique Continuation Property at the Boundary (SUCPB). Our approach is based on a suitable Carleman estimate, and involves an ad hoc reflection of the solution. We also give a simple application of our main result, by weakening the standard hypotheses ensuring uniqueness for the Cauchy problem for the plate equation.
2020
75
27
55
Goal 17: Partnerships for the goals
Morassi, Antonino ; Rosset, Edi ; Vessella, Sergio
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1218115
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