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

Donatella Danielli; Alaa Haj Ali

doi:10.1016/j.na.2021.112583

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

Donatella Danielli, Alaa Haj Ali

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

Abstract

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 (−Δ)^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.

Original language	English (US)
Article number	112583
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	214
DOIs	https://doi.org/10.1016/j.na.2021.112583
State	Published - Jan 2022

Keywords

Biharmonic operator
Free boundary problems
Monotonicity formulas
Variational methods

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.na.2021.112583

Cite this

@article{b9d113cd54b04d73b352f13c7171b7f7,

title = "A two phase boundary obstacle-type problem for the bi-Laplacian",

abstract = "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 (−Δ)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.",

keywords = "Biharmonic operator, Free boundary problems, Monotonicity formulas, Variational methods",

author = "Donatella Danielli and {Haj Ali}, Alaa",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2022",

month = jan,

doi = "10.1016/j.na.2021.112583",

language = "English (US)",

volume = "214",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Limited",

}

TY - JOUR

T1 - A two phase boundary obstacle-type problem for the bi-Laplacian

AU - Danielli, Donatella

AU - Haj Ali, Alaa

PY - 2022/1

Y1 - 2022/1

N2 - 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 (−Δ)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.

AB - 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 (−Δ)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.

KW - Biharmonic operator

KW - Free boundary problems

KW - Monotonicity formulas

KW - Variational methods

UR - http://www.scopus.com/inward/record.url?scp=85115010902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85115010902&partnerID=8YFLogxK

U2 - 10.1016/j.na.2021.112583

DO - 10.1016/j.na.2021.112583

M3 - Article

AN - SCOPUS:85115010902

SN - 0362-546X

VL - 214

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 112583

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this