Stable Equilibria to Elliptic Equations in Unbounded Domains with Nonlinear Dynamic Boundary Conditions

Analysis (Germany)

Volumn 20, Issue 4, 2000, Pages 325-352

  Escher, Joachim ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442704885     PISSN: 01744747     EISSN: 21966753     Source Type: Journal    
DOI: 10.1524/anly.2000.20.4.325     Document Type: Article

References (22)

1. R.A. Adams, Sobolev Spaces, Academic Press, New York, San Francisco, London, 1975.
2. S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand-Reinhold, Princeton, 1965.
3. H. Amann K. J. Escher, Analysis I, Birkauser, Basel, Boston, Berlin, 1998.
4. H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, Function Spaces, Differential Operators, and Nonlinear Analysis, H.J. Schmeisser, H. Triebel, editors, 1993, 9–126.
5. H. Amann, Linear and Quasilinear Parabolic Problems, Birkhauser, Basel, Boston, Berlin, 1995.
6. F. Browder, On the spectral theory of elliptic operators, Math. Ann., 142 (1962), 22130.
7. J. Escher, Nonlinear elliptic systems with dynamic boundary conditions, Math. Z., 210 (1992), 413–439.
8. J. Escher, The Dirichlet-Neumann operator on continuous functions, Annali Sc. Norm. Sup. Pisa, 21 (1994), 235–266.
9. J. Escher & G. Simonett, Analyticity of the interface in a free boundary problem Math. Ann., 305 (1996), 439–459.
10. J. Escher, B. Scarpellini, Stability properties of parabolic equations in unbounded domains, Arch. Math. 71 (1998), 31–45.
11. J. Escher & B. Scarpellini, On the asymptotics of solutions of parabolic equations on unbounded domains, Nonlinear Anal. 33 (1998), 483–507.
12. H. Fattorini, The Cauchy Problem, Addison-Wesley, Reading, MA, 1983.
13. D. Gilbarg & N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
14. G. Grubb, Functional Calculus of Pseudodifferential Boundary Problems, 2nd ed., Birkhauser, Basel, Boston, Berlin, 1996.
15. J.L. Lions & E. Magenes, Problemi ai limiti nonhomogenei (V), Ann. Scuola Norm. Sup. Pisa 16 (1962), 1–44.
16. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkauser, Basel, Boston, Berlin, 1995.
17. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, Heidelberg, New York, 1983.
18. B.E. Petersen, Introduction to the Fourier Transform and Pseudo-Differential Operators, Pitman, Boston, London, Melbourne, 1983.
19. M.H. Frotta & H.F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, 1967.
20. R. Redlinger, Uber die C2-Kompaktheit der Balm von Losungen semilinearer parabolischer Gleichungen, Proc. Roy. Soc. Edinb. 93 (1982), 99–103.
21. H. Triebei, Theory of Function Spaces II, Birkhauser, Basel, Boston, Berlin, 1992.
22. H. Triebei, T. Wloka, B. Rowley, & B. Lawruk, Boundary Value Problems for Elliptic Systems, Cambridge University Press, Cambridge, 1995.