Abstract
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 language | English (US) |
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Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | Mathematics In Engineering |
Volume | 3 |
Issue number | 1 |
DOIs | |
State | Published - 2021 |
Externally published | Yes |
Keywords
- Free boundary problems
- Monotonicity formulas
- Obstacle problems
- Penalized boundary conditions
- Semi-permeable membranes
ASJC Scopus subject areas
- Applied Mathematics
- Mathematical Physics
- Analysis