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Abstract: We show the existence and uniqueness of solutions either local or global forsmall data for an equation arising in different aspects of surface growth.Following the work of Koch and Tataru we consider spaces critical with respectto scaling and we prove our results in the largest possible critical space suchthat weak solutions are defined. The uniqueness of global weak solutionsremains unfortunately open, unless the initial conditions are sufficientlysmall.



Autor: Dirk Blomker, Marco Romito

Fuente: https://arxiv.org/







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