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- W4387076406 abstract "We capture optimal decay for the Mullins-Sekerka evolution, a nonlocal, parabolic free boundary problem from materials science. Our main result establishes convergence of BV solutions to the planar profile in the physically relevant case of ambient space dimension three. Far from assuming small or well-prepared initial data, we allow for initial configurations that do not have graph structure and in which the region of positive phase is not simply connected, hence explicitly including the regime of Ostwald ripening. In terms only of initially finite (not small) excess mass and surface energy, we establish that the surface becomes a Lipschitz graph within a fixed timescale (quantitatively estimated) and remains trapped within this setting for future times. To obtain the graph structure, we leverage regularity results from geometric measure theory. At the same time, we extend a duality method previously employed for one dimensional PDE problems to higher dimensional, nonlocal geometric evolutions. Optimal algebraic decay rates of excess energy, dissipation, and graph height are obtained." @default.
- W4387076406 created "2023-09-27" @default.
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- W4387076406 date "2023-09-25" @default.
- W4387076406 modified "2023-10-14" @default.
- W4387076406 title "Convergence to the planar interface for a nonlocal free-boundary evolution" @default.
- W4387076406 doi "https://doi.org/10.48550/arxiv.2309.14215" @default.
- W4387076406 hasPublicationYear "2023" @default.
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