Further regularity and uniqueness results for a non-isothermal Cahn--Hilliard equation
- Ipocoana, Erica
- Zafferi, Andrea
2010 Mathematics Subject Classification
- 35Q35 35D35 80A22 35A02 35B65
- Cahn--Hilliard, non-isothermal model, regularity of solutions, uniqueness
The aim of this paper is to establish new regularity results for a non-isothermal Cahn--Hilliard system in the two-dimensional setting. The main achievement is a crucial L∞ estimate for the temperature, obtained by a suitable Moser iteration scheme. Our results in particular allow us to get a new simplified version of the uniqueness proof for the considered model.
- Commun. Pure Appl. Anal., 20 (2021), pp. 763--782, DOI 10.3934/cpaa.2020289 .