The Kurdyka–Łojasiewicz–Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems
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- by Ralph Chill and Sebastian Mildner PDF
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Abstract:
We state and reprove a stabilisation result for solutions of abstract gradient systems associated with nonsmooth energy functions on infinite- dimensional Hilbert spaces. The main feature is the introduction of a convenient topology on the effective domain of the energy function, and that in this general setting the usual assumption on the relative compactness of the range of the solution in the energy space can be considerably relaxed to relative compactness of the range in the ambient Hilbert space. This simplifies the applicability of the stabilisation result even in the case of smooth energies.References
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Additional Information
- Ralph Chill
- Affiliation: Institut für Analysis, Technische Universität Dresden, 01062 Dresden, Germany
- MR Author ID: 628534
- Email: ralph.chill@tu-dresden.de
- Sebastian Mildner
- Affiliation: Institut für Analysis, Technische Universität Dresden, 01062 Dresden, Germany
- MR Author ID: 1173590
- Email: sebastian.mildner@tu-dresden.de
- Received by editor(s): September 9, 2016
- Received by editor(s) in revised form: February 14, 2017, and December 22, 2017
- Published electronically: May 4, 2018
- Communicated by: Yingfei Yi
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4307-4314
- MSC (2010): Primary 34A60, 26D10; Secondary 47J35, 49J52
- DOI: https://doi.org/10.1090/proc/14067
- MathSciNet review: 3834660