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

Robert Denk, Matthias Georg Hieber, Jan Prüss

研究成果: Article査読

154 被引用数 (Scopus)

抄録

In this paper we investigate vector-valued parabolic initial boundary value problems A(t,x,D), Bj(t,x,D) subject to general boundary conditions in domains G in ℝn with compact C 2m -boundary. The top-order coefficients of A 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 A and the Lopatinskii-Shapiro condition on A, B1... Bm) 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.

本文言語English
ページ(範囲)193-224
ページ数32
ジャーナルMathematische Zeitschrift
257
1
DOI
出版ステータスPublished - 2007 9
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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