Analyticity of solutions to fully nonlinear parabolic evolution equations on symmetric spaces

Journal of Evolution Equations

Volumn 3, Issue 4, 2003, Pages 549-576

  Escher, Joachim ^a   Simonett, Gieri ^b  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1642325884     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-003-0093-z     Document Type: Article

References (28)

1. AMANN, H., Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in H. J. Schmeisser, H. Triebel, editors, Function Spaces, Differential Operators and Nonlinear Analysis, Teubner, Stuttgart, Leipzig, 1993, 9-126.
2. AMANN, H., Linear and Quasilinear Parabolic Problems, Vol. I, Birkhäuser, Basel, 1995.
3. AMANN, H., Elliptic operators with infinite-dimensional state spaces. J. Evol. Equs. 1 (2001), 143-188.
4. AMANN, H. and ESCHER, J., Analysis III, Birkhäuser, Basel, 2001.
5. ANGENENT, S., Nonlinear analytic semiflows. Proc. Roy. Soc. Edinburgh 115A (1990), 91-107.
6. AUBIN, T., Nonlinear Analysis on Manifolds. Monge-Ampére Equations. Springer, New York, 1992.
7. BAILLON, J. B., Caractère borné de certains générateurs de semigroup linéaire dans les espaces de Banach. CR. Acad. Sc. Paris 290A (1980), 757-760.
8. CAHN, J. W. and TAYLOR J. E., Surface motion by surface diffusion. Acta Metallurgica 42 (1994), 1045-1063.
9. DA PRATO, G. and GRISVARD, P., Equations d'évolution abstraites nonlinéaires de type parabolique. Ann. Mat. Pura Appl. 120 (1979), 329-396.
10. EIDELMAN, S. D., Parabolic Systems. North-Holland, Amsterdam, 1969.
11. ESCHER, J. and SIMONETT, G., Analyticity of the interface in a free boundary problem. Math. Ann. 305 (1996), 439-459.
12. ESCHER, J. and SIMONETT, G., Classical solutions of multidimensional Hele-Shaw models. SIAM J. Math. Anal. 28, 1028-1047.
13. ESCHER, J. and SIMONETT, G., A center manifold analysis for the Mullins-Sekerka model. J. Differential Equations 143 (1998), 267-292.
14. ESCHER, J., MAYER, U. F. and SIMONETT, G., The surface diffusion flow for immersed hypersurfaces. SIAM J. Math. Anal. 29 (1999), 1419-1433.
15. ESCHER, J., SIMONETT, G. and PRÜSS, J., A new approach to the regularity of solutions for parabolic equations. In Evolution Equations: Proceedings in Honour of J. A. Goldstein's 60th Birthday, M. Dekker, to appear.
16. FRIEDMAN, A., Partial Differential Equations. Krieger, New York, 1976.
17. HELGASON, S., Differential Geometry and Symmetric spaces. Academic Press, New York, 1962.
18. HENRY, D., Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. 840, Springer, Berlin (1981).
19. KLINGENBERG, W., Riemannian Geometry, de Gruyter, Berlin 1982.
20. KOBAYASHI, S. and NOMIZU, K., Foundations of Differential Geometry. Wiley, New York 1963.
21. LADYZENSKAJA, O. A., SOLONNIKOV, V. A. and URALCEVA N. N., Linear and Quasilinear Equations of Parabolic Type, AMS, Providence, Rhode Island, 1968.
22. LUNARDI, A., Analytic Semigroups and Optimal Regularity in Parabolic Equations. Birkhäuser, Basel, 1991.
23. PETERSEN, B. E., Introduction to the Fourier Transform and Pseudo-Differential Operators. Pitman, Boston, 1983.
24. B. Amer. J. Math. 93 (1971), 299-309.
25. SIMONETT, G., Center manifolds for quasilinear reaction-diffusion systems. Differential Integral Equations 8 (1995), 753-796.
26. TRIEBEL, H., Theory of Function Spaces. Birkhäuser, Basel, 1983.
27. TRIEBEL, H., Theory of Function Spaces II. Birkhäuser, Basel, 1992.
28. YOSIDA, K., Functional Analysis. Springer, Berlin, 1980.