PreprintCC BY 4.0arXiv
An H-convergence-based implicit function theorem for homogenization of nonlinear non-smooth elliptic systems
Abstract
We consider homogenization of Dirichlet problems for semilinear elliptic systems with non-smooth data. We suppose that the diffusion tensors H-converge if the homogenization parameter tends to zero. Our result is of implicit function theorem type: For small homogenization parameter there exists exactly one weak solution close to a given non-degenerate weak solution to the homogenized problem. For the proofs we use gradient estimates of Meyers (if the space dimension is two) or Morrey (if the diffusion tensors are triangular) type for solutions to linear elliptic systems.
Versions
Related
- Nonlinear elliptic homogenization with the parametric Deep Ritz method
- A semi-generating function approach to the stability of implicit-explicit multistep methods for nonlinear parabolic equations
- On regularity of averaged Green's functions in homogenization of elliptic PDE
- A Tensor Neural Network Method for High-Order Homogenization of Locally Periodic Elliptic Problems
- Convergence rates in the periodic homogenization of vanishing-viscous Hamilton-Jacobi equations
BibTeX
@misc{recke2026hconvergencebased,
title = {{An H-convergence-based implicit function theorem for homogenization of nonlinear non-smooth elliptic systems}},
author = {Lutz Recke},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.11976},
eprint = {2605.11976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.11976},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An H-convergence-based implicit function theorem for homogenization of nonlinear non-smooth elliptic systems
AU - Lutz Recke
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2605.11976
UR - https://arxiv.org/abs/2605.11976
AB - We consider homogenization of Dirichlet problems for semilinear elliptic systems with non-smooth data. We suppose that the diffusion tensors H-converge if the homogenization parameter tends to zero. Our result is of implicit function theorem type: For small homogenization parameter there exists exactly one weak solution close to a given non-degenerate weak solution to the homogenized problem. For the proofs we use gradient estimates of Meyers (if the space dimension is two) or Morrey (if the diffusion tensors are triangular) type for solutions to linear elliptic systems.
ER -