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

Donatella Danielli, Alaa Haj Ali

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number112583
JournalNonlinear Analysis, Theory, Methods and Applications
StatePublished - Jan 2022


  • Biharmonic operator
  • Free boundary problems
  • Monotonicity formulas
  • Variational methods

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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