Optimal L p - L q -estimates for parabolic boundary value problems with inhomogeneous data

Author： Denk Robert  

Publisher： Springer Publishing Company

ISSN： 0025-5874

Source： Mathematische Zeitschrift, Vol.257, Iss.1, 2007-09, pp. : 193-224

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Abstract

In this paper we investigate vector-valued parabolic initial boundary value problems , subject to general boundary conditions in domains G in with compact C 2m -boundary. The top-order coefficients of are assumed to be continuous. We characterize optimal L p -L q -regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on and the Lopatinskii–Shapiro condition on are necessary for these L p -L q -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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