WIAS Preprint No. 1459, (2009)

Maximal parabolic regularity for divergence operators on distribution spaces


  • Haller-Dintelmann, Robert
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35A05 35B6 35K15 35K20


  • Maximal parabolic regularity, quasilinear parabolic equations, mixed Dirichlet--Neumann conditions


We show that elliptic second order operators A of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of A are discontinuous and A is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth data are presented.

Appeared in

  • Parabolic Problems: The Herbert Amann Festschrift, J. Escher, P. Guidotti, M. Hieber, P. Mucha, J.W. Pruess, Y. Shibata, G. Simonett, CH. Walker, W. Zajaczkowski, eds., vol. 80 of Progress in Nonlinear Differential Equations and Their Applications, Springer, Basel, 2011, pp. 313--342

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