Lp-estimates for a transmission problem of mixed elliptic-parabolic type
R. Denk and T. Seger
Abstract. We consider the situation when an elliptic problem in a subdomain Ω1 of an n-dimensional bounded domain Ω is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in Ω\Ω1. In particular, we can treat elliptic-parabolic equations in bounded domains with discontinuous coefficients. Using Fourier multiplier techniques, we prove an a priori estimate for strong solutions to the equations in Lp-Sobolev spaces.
Bound. Value Probl. 2014:22 (23 pp.)
doi:10.1186/1687-2770-2014-22
The paper is available here (final version).