Classical solutions for diffusion-induced grain-boundary motion

Uwe F. Mayer and Gieri Simonett

Abstract: We prove existence and uniqueness of classical solutions for the motion of hypersurfaces driven by mean curvature and diffusion of a solute along the surface. This free boundary problem involves solving a coupled system of fully nonlinear partial differential equations.

Key words: Free boundary problem, mean curvature, DIGM, system of fully nonlinear PDEs, maximal regularity.

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