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L<sup>p</sup>-estimates for a transmission problem of mixed elliptic-parabolic type

Lp-estimates for a transmission problem of mixed elliptic-parabolic type

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DENK, Robert, Tim SEGER, 2013. Lp-estimates for a transmission problem of mixed elliptic-parabolic type

@techreport{Denk2013estim-24165, series={Konstanzer Schriften in Mathematik}, title={Lp-estimates for a transmission problem of mixed elliptic-parabolic type}, year={2013}, number={318}, author={Denk, Robert and Seger, Tim} }

2013 Seger, Tim Seger, Tim Denk, Robert Denk, Robert 2013-08-09T08:22:47Z eng terms-of-use L<sup>p</sup>-estimates for a transmission problem of mixed elliptic-parabolic type 2013-08-09T08:22:47Z We consider the situation when an elliptic problem in a subdomain &Omega;<sub>1</sub> of an n-dimensional bounded domain &Omega; is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in &Omega;\&Omega;<sub>1</sub>. 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<sup>p</sup>-Sobolev spaces.

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