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On the homogenization of a class of nonlinear operators with variable periodic rapidly oscillating exponent

  • Maria-Magdalena Boureanu
  • Renata Bunoiu
  • Claudia Timofte
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Abstract

We study the homogenization of a class of nonlinear elliptic problems governed by Leray-Lions type operators, with variable periodic rapidly oscillating exponent and satisfying nonstandard coercivity and growth conditions. The operators involved in our analysis include as particular examples generalized Laplace, mean curvature, and capillarity operators, along with sums of these operators. Therefore, our results provide a unified approach for several nonlinear models related to various applications. Combining, in a novel way, different techniques, such as the two-scale convergence method in variable exponent spaces and suitable convexity results, we derive the homogenized limit problem.

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Cite

BibTeXRIS
BibTeX
@misc{boureanu2026homogenization,
  title = {{On the homogenization of a class of nonlinear operators with variable periodic rapidly oscillating exponent}},
  author = {Maria-Magdalena Boureanu and Renata Bunoiu and Claudia Timofte},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05757890v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On the homogenization of a class of nonlinear operators with variable periodic rapidly oscillating exponent
AU  - Maria-Magdalena Boureanu
AU  - Renata Bunoiu
AU  - Claudia Timofte
PY  - 2026
DA  - 2026/09/18
PB  - HAL
UR  - https://hal.science/hal-05757890v1
AB  - We study the homogenization of a class of nonlinear elliptic problems governed by Leray-Lions type operators, with variable periodic rapidly oscillating exponent and satisfying nonstandard coercivity and growth conditions. The operators involved in our analysis include as particular examples generalized Laplace, mean curvature, and capillarity operators, along with sums of these operators. Therefore, our results provide a unified approach for several nonlinear models related to various applications. Combining, in a novel way, different techniques, such as the two-scale convergence method in variable exponent spaces and suitable convexity results, we derive the homogenized limit problem.
ER  -