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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

Type of Publication: Working Paper/Technical Report
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-241650
Author: Denk, Robert; Seger, Tim
Year of publication: 2013
Series: Konstanzer Schriften in Mathematik ; 318
Summary:
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.
MSC Classification: 35B45, 35M12
Subject (DDC): 510 Mathematics
Keywords: Transmission problem, elliptic-parabolic equation, a priori estimates
Link to License: In Copyright
Bibliography of Konstanz: Yes

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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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