Graphical mean curvature flow with zero boundary data is locally well-posed for approximable Lipschitz graphs, globally well-posed for small initial slopes, and decays exponentially on bounded domains.
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Well-posedness for the mean curvature flow on the half-space and on bounded domains
Graphical mean curvature flow with zero boundary data is locally well-posed for approximable Lipschitz graphs, globally well-posed for small initial slopes, and decays exponentially on bounded domains.