We consider the nonlocal Cahn-Hilliard equation with singular potential and degenerate mobility in a bounded domain Ω⊂R^d, d≤3. We first prove the existence of maximal strong solutions in weighted (in time) L^p spaces. Then we establish further regularity properties of the solution through maximal regularity theory. Finally, we revisit the separation property in an appendix.
Regularity results for the nonlocal Cahn-Hilliard equation with singular potential and degenerate mobility
M. Grasselli
2021-01-01
Abstract
We consider the nonlocal Cahn-Hilliard equation with singular potential and degenerate mobility in a bounded domain Ω⊂R^d, d≤3. We first prove the existence of maximal strong solutions in weighted (in time) L^p spaces. Then we establish further regularity properties of the solution through maximal regularity theory. Finally, we revisit the separation property in an appendix.File in questo prodotto:
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