Motion of elastic thin films by anisotropic surface diffusion with curvature regularization. (English) Zbl 1270.74127
Summary: We prove short time existence, uniqueness and regularity for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained two-dimensional films. This is achieved by using the \(H^{-1}\)-gradient flow structure of the evolution law, via De Giorgi’s minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.
MSC:
| 74K35 | Thin films |
| 74H20 | Existence of solutions of dynamical problems in solid mechanics |
| 74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
| 74H30 | Regularity of solutions of dynamical problems in solid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
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