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

Denk, Robert; Seger, Tim

doi:10.1186/1687-2770-2014-22

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L^p-estimates for a transmission problem of mixed elliptic-parabolic type

Type of Publication:	Journal article
URI (citable link):	http://nbn-resolving.de/urn:nbn:de:bsz:352-280617
Author:	Denk, Robert; Seger, Tim
Year of publication:	2014
Published in:	Boundary Value Problems ; 2014 (2014), 1. - 22. - ISSN 1687-2770. - eISSN 1687-2770
DOI (citable link):	https://dx.doi.org/10.1186/1687-2770-2014-22
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 L^p-Sobolev spaces.
MSC Classification:	35B45; 35M12
Subject (DDC):	510 Mathematics
Keywords:	Transmission problem, elliptic-parabolic equation, a priori estimates
Link to License:	Attribution 2.0 Generic
Bibliography of Konstanz:	Yes

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DENK, Robert, Tim SEGER, 2014. L^p-estimates for a transmission problem of mixed elliptic-parabolic type. In: Boundary Value Problems. 2014(1), 22. ISSN 1687-2770. eISSN 1687-2770. Available under: doi: 10.1186/1687-2770-2014-22

@article{Denk2014estim-28061, title={L^p-estimates for a transmission problem of mixed elliptic-parabolic type}, year={2014}, doi={10.1186/1687-2770-2014-22}, number={1}, volume={2014}, issn={1687-2770}, journal={Boundary Value Problems}, author={Denk, Robert and Seger, Tim}, note={Article Number: 22} }

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. Denk, Robert Seger, Tim 2014 Seger, Tim Attribution 2.0 Generic eng Lp-estimates for a transmission problem of mixed elliptic-parabolic type 2014-06-13T07:14:29Z Boundary value problems ; (2014). - 22 Denk, Robert 2014-06-13T07:14:29Z