Abstract
In this note we present some constructions with generators of analytic semigroups which are an abstract version of the familiar method of “freezing the coefficients” to prove elliptic estimates for differential operators with continuous coefficients or Hölder-continuous coefficients. As a side result we obtain an abstract exponential decay result for, say, eigenfunctions corresponding to isolated eigenvalues.
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
Amann, H., “Quasilinear evolution equations and parabolic systems”, TAMS 293 (1986), 191–227.
[2] Amann, H., “On abstract parabolic fundamental solutions”, J. Math. Soc. Japan, 39 (1987).
Amann, H., “Quasilinear parabolic systems under nonlinear boundary conditions”, Arch. Rat. Mech. Anal. 92 (1986), 153–192.
Amann, H., Linear and Quasilinear Parabolic Problems, Vol I, Birkhäuser, 1995, Vol II, to appear.
Amann, H., Hieber, M., Simonett, G.: “Bounded H ∞-calculus for elliptic operators”, Differential and Integral Equations 7 (1994), 613–653.
[6] Angenent, S.B., “Nonlinear Analytic Semiflows”, Proceedings of the Royal Society in Edinburgh 115A (1990) pp. 91–107.
Angenent, S.B., “The shadowing lemma for elliptic PDE”, pp. 7–22 in “Dynamics of Infinite dimensional dynamical systems,” NATO/ASI series F, vol.37, Springer Verlag.
Angenent, S.B., “A variational interpretation of Melnikov’s function and exponentially small separatrix splitting”, pp. 5–35 in “Symplectic Geometry,” London Mathematical Society Lecture Note Series vol. 192, Cambridge University Press (1993)
Bergh, J. and Löfström, J., Interpolation Spaces, an Introduction, Springer Verlag, Berlin, 1976.
Butzer, P.L. and Berens, H., Semigroups of Operators and Approximation, Springer Verlag, Berlin, 1967.
Clément, Ph., Heijmans, H.J.A.M., et. al., One Parameter Semigroups, CWI Monographs #5, North Holland, Amsterdam, 1987.
DaPrato, G. and Grisvard, P., “Équations d’évolutions abstraites nonlinéaires de type parabolique”, Annali di Mat. Pura ed Appl, 120 (1979), 329–396.
Lunardi, A., “Quasilinear parabolic equations”, Math. Annalen 267 (1984), 395–415.
Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam, 1978.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Basel AG
About this chapter
Cite this chapter
Angenent, S. (1999). Constructions with Analytic Semigroups and Abstract Exponential Decay Results for Eigenfunctions. In: Escher, J., Simonett, G. (eds) Topics in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 35. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8765-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8765-6_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9764-8
Online ISBN: 978-3-0348-8765-6
eBook Packages: Springer Book Archive