L p -estimates for a transmission problem of mixed elliptic-parabolic type
Robert Denk, Tim Seger · Boundary Value Problems · 2014
We consider the situation when an elliptic problem in a subdomain 1 of an n-dimensional bounded domain is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in \ 1 .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 L p -Sobolev spaces.