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

被引：8

作者：

Alessandrini, Giovanni ^{[1
]}

Rosset, Edi ^{[1
]}

Vessella, Sergio ^{[2
]}

机构：

[1] Univ Trieste, Dipartimento Matemat & Geosci, Via Valerio 12-1, I-34127 Trieste, Italy

[2] Univ Firenze, Dipartimento Matemat & Informat Ulisse Dini, Viale Morgagni 67-a, I-50134 Florence, Italy

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2019年 / 231卷 / 03期

关键词：

STRONG UNIQUE CONTINUATION; QUANTITATIVE UNIQUENESS; INCLUSIONS; STABILITY; CAVITIES; DOMAINS;

D O I：

10.1007/s00205-018-1302-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1455 / 1486

页数：32