Maximal Regularity of Parabolic Transmission Problems
Herbert Amann
TL;DR
This paper proves that linear reaction-diffusion equations with complex boundary and transmission conditions have maximal Lp regularity, even when the transmission interface intersects the domain boundary transversally.
Contribution
It introduces a novel analysis allowing the transmission interface to intersect the boundary transversally, extending maximal regularity results to more complex geometries.
Findings
Maximal Lp regularity is established for reaction-diffusion equations with inhomogeneous boundary and transmission conditions.
The analysis accommodates interfaces intersecting the boundary transversally.
The results extend the applicability of maximal regularity theory to more general geometrical configurations.
Abstract
Linear reaction-diffusion equations with inhomogeneous boundary and transmission conditions are shown to possess the property of maximal Lp regularity. The new feature is the fact that the transmission interface is allowed to intersect the boundary of the domain transversally.
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