-estimates for a transmission problem of mixed elliptic-parabolic type
Department of Mathematics and Statistics, University of Konstanz, Konstanz, 78457, Germany
Boundary Value Problems 2014, 2014:22 doi:10.1186/1687-2770-2014-22Published: 22 January 2014
We consider the situation when an elliptic problem in a subdomain of an n-dimensional bounded domain Ω is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in . 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 -Sobolev spaces.
MSC: 35B45, 35M12.