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@unpublished{Denk2005Optim-648, year={2005}, title={Optimal Lp-Lq-regularity for parabolic problems with inhomogeneous boundary data}, author={Denk, Robert and Hieber,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