WIAS Preprint No. 1712, (2012)

Parabolic equations with dynamical boundary conditions and source terms on interfaces



Authors

  • ter Elst, A.F.M.
  • Meyries, Martin
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35K20 35K59 35M13 35R05

Keywords

  • Parabolic equation, quasilinear parabolic problem, mixed boundary condition, dynamical boundary condition, maximal parabolic Lp-regularity, nonsmooth geometry, nonsmooth coefficients

Abstract

We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regularity assumptions on the domain and the coefficients are imposed. It is shown that the corresponding linear operator enjoys maximal parabolic regularity in a suitable Lp-setting. The linear results suffice to treat also the corresponding nondegenerate quasilinear problems.

Appeared in

  • Ann. Mat. Pura Appl. IV. Ser., 193 (2014) pp. 1295--1318.

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