DOI: 10.3390/math14213892 ISSN: 2227-7390
Homogenization of a Monotone Robin Problem in a Domain with a Thick Oscillating Boundary
Patrizia Donato, Klas PetterssonIn this paper, the asymptotics of an elliptic boundary value problem in two dimensions with a thick oscillating boundary Γε are characterized, as the period of oscillations ε tends to zero. On Γε, a nonlinear Robin boundary condition is prescribed, where the nonlinear function is monotone, regular, and of polynomial growth. The asymptotics depend on both the geometric oscillations and the rapidly oscillating coefficients of the differential operator. The methods of Minty for monotone operators, together with periodic unfolding adapted to the problem domain, introduced in a previous paper by the authors, are applied. The homogenized problem is described, as well as the convergence of the energies.