L1-Contraction and Uniqueness for Quasilinear Elliptic–Parabolic Equations

@article{Otto1995L1ContractionAU,
  title={L1-Contraction and Uniqueness for Quasilinear Elliptic–Parabolic Equations},
  author={Felix Otto},
  journal={Journal of Differential Equations},
  year={1995},
  volume={131},
  pages={20-38}
}
  • F. Otto
  • Published 10 October 1996
  • Mathematics
  • Journal of Differential Equations
Abstract We prove the L 1 -contraction principle and uniqueness of solutions for quasilinear elliptic–parabolic equations of the form[formula]where b is monotone nondecreasing and continuous. We assume only that u is a weak solution of finite energy. In particular, we do not suppose that the distributional derivative ∂ t [ b ( u )] is a bounded Borel measure or a locally integrable function. 
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