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

Robert Denk; Tim Seger

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

Analysis of PDEs 2017-06-23 v1

Authors: Robert Denk , Tim Seger

Abstract

We consider the situation when an elliptic problem in a subdomain $\Omega_1$ of an $n$ -dimensional bounded domain $\Omega$ is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in $\Omega\setminus\Omega_1$ . 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.

Keywords

transmission problem mixed elliptic-parabolic type $L^p$-estimates discontinuous coefficients Fourier multiplier techniques a priori estimate $L^p$-Sobolev spaces

Cite

@article{arxiv.1311.5775,
  title  = {$L^p$-estimates for a transmission problem of mixed elliptic-parabolic type},
  author = {Robert Denk and Tim Seger},
  journal= {arXiv preprint arXiv:1311.5775},
  year   = {2017}
}

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