Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data

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2005
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Hieber, Matthias
Prüss, Jan
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In this paper we investigate vector-valued parabolic initial boundary value problems (A(x,D), B1(x,D),..., Bm(x,D)) subject to general boundary conditions in a domain G with compact boundary. The top-order coefficients of the operator A are assumed to be continuous. We characterize optimal Lp-Lq-regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on A and the Lopatinskii-Shapiro condition on (A(x,D), B1(x,D),..., Bm(x,D)) are necessary for these Lp-Lq-estimates. As a byproduct of the techniques being introduced we obtain new trace and extension results for Sobolev spaces of mixed order and a characterization of Triebel-Lizorkin spaces by boundary data.

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ISO 690DENK, Robert, Matthias HIEBER, Jan PRÜSS, 2005. Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data
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@unpublished{Denk2005Optim-648,
  year={2005},
  title={Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data},
  author={Denk, Robert and Hieber, Matthias and Prüss, Jan}
}
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