PreprintarXiv licencearXiv
On the elliptic regularization of maximal slope curves
Abstract
We consider the so-called Weighted Energy-Dissipation approximation of gradient flows in metric spaces. We prove the convergence of minimizers to maximal slope curves under assumptions that are close to those of the original existence theory for metric gradient flows. The proof relies on an energy-dissipation identity for the approximating curves and on an adaptation of a general stability result for maximal slope curves.
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BibTeX
@misc{gobbino2026elliptic,
title = {{On the elliptic regularization of maximal slope curves}},
author = {Massimo Gobbino and Filippo Quattrocchi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08377},
eprint = {2611.08377},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08377},
}
RIS
TY - UNPB
TI - On the elliptic regularization of maximal slope curves
AU - Massimo Gobbino
AU - Filippo Quattrocchi
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08377
UR - https://arxiv.org/abs/2611.08377
AB - We consider the so-called Weighted Energy-Dissipation approximation of gradient flows in metric spaces. We prove the convergence of minimizers to maximal slope curves under assumptions that are close to those of the original existence theory for metric gradient flows. The proof relies on an energy-dissipation identity for the approximating curves and on an adaptation of a general stability result for maximal slope curves.
ER -