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Peer-reviewedCC BY 4.0Mathematics

Homogenization of a Monotone Robin Problem in a Domain with a Thick Oscillating Boundary

  • Patrizia Donato1
  • Klas Pettersson2
  1. 1Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS, Université Rouen Normandie, F-76000 Rouen, France
  2. 2Independent Researcher, SE-435 39 Mölnlycke, Sweden
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Abstract

In 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.

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Cite

BibTeXRIS
BibTeX
@article{donato2026homogenization,
  title = {{Homogenization of a Monotone Robin Problem in a Domain with a Thick Oscillating Boundary}},
  author = {Patrizia Donato and Klas Pettersson},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213892},
  url = {https://www.mdpi.com/2227-7390/14/21/3892},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Homogenization of a Monotone Robin Problem in a Domain with a Thick Oscillating Boundary
AU  - Patrizia Donato
AU  - Klas Pettersson
PY  - 2026
DA  - 2026/10/25
JO  - Mathematics
DO  - 10.3390/math14213892
UR  - https://www.mdpi.com/2227-7390/14/21/3892
AB  - In 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.
SN  - 2227-7390
ER  -