Garcke, Harald and Knopf, Patrik and Wittmann, Julia (2023) The anisotropic Cahn–Hilliard equation: Regularity theory and strict separation properties. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 16 (12). pp. 3622-3660. ISSN 1937-1632, 1937-1179
Full text not available from this repository.Abstract
The Cahn-Hilliard equation with anisotropic energy contributions frequently appears in many physical systems. Systematic analytical results for the case with the relevant logarithmic free energy have been missing so far. We close this gap and show existence, uniqueness, regularity, and separation properties of weak solutions to the anisotropic Cahn-Hilliard equation with logarithmic free energy. Since firstly, the equation becomes highly non-linear, and secondly, the relevant anisotropies are non-smooth, the analysis becomes quite involved. In particular, new regularity results for quasilinear elliptic equations of second order need to be shown.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PHASE-FIELD MODEL; SINGULAR PERTURBATIONS; VARIATIONAL-PROBLEMS; SHARP; MOTION; LIMIT; Cahn-Hilliard equation; anisotropy; weak solutions; regularity; sepa-ration property |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Mar 2024 06:00 |
| Last Modified: | 01 Mar 2024 06:00 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59211 |
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