Parabolic equations with dynamical boundary conditions and source terms on interfaces

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 $L^p$-setting. The linear results suffice to treat also the corresponding nondegenerate quasilinear problems.

30 pages. Revised version. To appear in Annali di Matematica Pura ed Applicata