• Corpus ID: 119749808

Regularizing effect of homogeneous evolution equations: case homogeneous order zero

  title={Regularizing effect of homogeneous evolution equations: case homogeneous order zero},
  author={Daniel Hauer and Jos{\'e} M. Maz{\'o}n},
  journal={arXiv: Analysis of PDEs},
In this paper, we develop a functional analytical theory for establishing that mild solutions of first-order Cauchy problems involving homogeneous operators of order zero are strong solutions; in particular, the first-order time derivative satisfies a global regularity estimate depending only on the initial value and the positive time. We apply those results to the Cauchy problem associated with the total variational flow operator and the nonlocal fractional 1-Laplace operator. 



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