Regularity results for a penalized boundary obstacle problem

Donatella Danielli, Rohit Jain

Research output: Contribution to journalArticlepeer-review


In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish structural properties of the free boundary. A central role is played by the monotonicity of ad hoc Almgren- and Monneau-type functionals.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalMathematics In Engineering
Issue number1
StatePublished - 2021
Externally publishedYes


  • Free boundary problems
  • Monotonicity formulas
  • Obstacle problems
  • Penalized boundary conditions
  • Semi-permeable membranes

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Analysis


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