Towards an L1-theory for vector-valued elliptic boundary value problems
R. Denk, M. Hieber, J. Prüss
Abstract. In this note, we consider vector-valued boundary value problems with constant coefficients in the L1-setting for a half space. We assume the Lopatinskii-Shapiro condition to be true and obtain a representation of the solution u of the elliptic problem by integral operators which allows to deduce a-priori estimates for u in the L1-norm. These estimates imply in particular that the L1-realization of an elliptic boundary value problem with constant coefficients in the half space generates an analytic C0-semigroup.
Progr. Nonlinear Differential Equations Appl. 55 (2003), 141-147.
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