Parabolic equations with dynamical boundary conditions and source terms on interfaces
Analysis of PDEs
2013-02-05 v2
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 -setting. The linear results suffice to treat also the corresponding nondegenerate quasilinear problems.
Keywords
Cite
@article{arxiv.1206.0600,
title = {Parabolic equations with dynamical boundary conditions and source terms on interfaces},
author = {A. F. M. ter Elst and Martin Meyries and Joachim Rehberg},
journal= {arXiv preprint arXiv:1206.0600},
year = {2013}
}
Comments
30 pages. Revised version. To appear in Annali di Matematica Pura ed Applicata