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Parabolic equations with dynamical boundary conditions and source terms on interfaces |
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| Authors: | A F M ter Elst M Meyries J Rehberg |
| Institution: | 1. Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand 2. Department of Mathematics, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany 3. Weierstrass Institute, Mohrenstr. 39, 10117, Berlin, Germany |
| 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. |
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