WIAS Preprint No. 1712, (2012)
Parabolic equations with dynamical boundary conditions and source terms on interfaces
- ter Elst, A.F.M.
- Meyries, Martin
- Rehberg, Joachim
2010 Mathematics Subject Classification
- 35K20 35K59 35M13 35R05
- Parabolic equation, quasilinear parabolic problem, mixed boundary condition, dynamical boundary condition, maximal parabolic Lp-regularity, nonsmooth geometry, nonsmooth coefficients
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.
- Ann. Mat. Pura Appl. IV. Ser., 193 (2014) pp. 1295--1318.