Archive for Rational Mechanics and Analysis

, Volume 231, Issue 3, pp 1455–1486 | Cite as

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

  • Giovanni AlessandriniEmail author
  • Edi Rosset
  • Sergio Vessella


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.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e GeoscienzeUniversità degli Studi di TriesteTriesteItaly
  2. 2.Dipartimento di Matematica e Informatica “Ulisse Dini”Università degli Studi di FirenzeFirenzeItaly

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