Regularity results for a penalized boundary obstacle problem

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.

Keywords

• free boundary problems
• obstacle problems
• penalized boundary conditions
• monotonicity formulas
• semi-permeable membranes