Abstract
Vector-valued elliptic and parabolic boundary value problems subject to general boundary conditions have been investigated recently in [DHP01] in the L p-context for 1 < p < oo. One of the main goals of this paper was to deduce a maximal L p -regularity result for the solution of the parabolic initial boundary value problem. A classical reference in the elliptic context are the celebrated papers of Agmon, Douglis and Nirenberg [ADN59]. For further references and information on the scalar and vector-valued case we refer to the [Ama01] and the list of references given in [DHP01].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I..Comm. Pure Appl. Math. 22 (1959) 623–727. II. Comm. Pure Appl. Math. 17 (1964), 623–727.
H. Amann, Dual semigroups and second order linear elliptic boundary value problems. Israel J. Math. 45 (1983), 225–254.
H.Amann, Elliptic operators with infinite-dimensional state spaces. J. Evol. Equ. 1 (2001), 143–188.
H. Amann, J. Escher, Strongly continuous dual semigroups. Ann. Mat. Pura Appl. CLXXI (1996), 41–62.
R. Denk, M. Hieber, J. Prüss, R.-boundedness, Fourier multipliers and problems of elliptic and parabolic type. Memoirs Amer. Math. Soc., to appear.
G. Di Blasio, Analytic semigroups generated by elliptic operators in Ll and parabolic equations. Osaka J. Math. 28 (1991), 367–384.
D. Guidetti, On elliptic systems in Ll. Osaka J. Math. 30 (1993), 397–429.
H. Tanabe, Functional Analytic Methods for Partial Differential Equations. Marcel Dekker, New York, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Basel AG
About this paper
Cite this paper
Denk, R., Hieber, M., Prüss, J. (2003). Towards an L 1-Theory for Vector-Valued Elliptic Boundary Value Problems. In: Iannelli, M., Lumer, G. (eds) Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics. Progress in Nonlinear Differential Equations and Their Applications, vol 55. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8085-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8085-5_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9433-3
Online ISBN: 978-3-0348-8085-5
eBook Packages: Springer Book Archive