A two phase boundary obstacle-type problem for the bi-Laplacian

被引：1

作者：

Danielli, Donatella ^{[1
]}

Ali, Alaa Haj ^{[2
]}

机构：

[1] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2022年 / 214卷

关键词：

Free boundary problems; Variational methods; Biharmonic operator; Monotonicity formulas; REGULARITY;

D O I：

10.1016/j.na.2021.112583

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we are concerned with a two phase boundary obstacle-type problem for the bi-Laplace operator in the upper unit ball. The problem arises in connection with unilateral phenomena for flat elastic plates. It can also be seen as an extension problem to an obstacle problem for the fractional Laplacian (-Delta)(3/2), as first observed in Yang (2013). We establish the well-posedness and the optimal regularity of the solution, and we study the structure of the free boundary. Our proofs are based on monotonicity formulas of Almgren- and Monneau-type. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：26

共 23 条

[1] Regularity of the free boundary in the biharmonic obstacle problem [J].