The Dirichlet-Neumann operator on continuous functions

Escher, Joachim

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 21 (1994) no. 2, pp. 235-266

[1] R.A. Adams, Sobolev Spaces. Academic Press, New York-London, 1975. | Zbl | MR

[2] M. Altman-D.P. Altman.P Ross - H. Chang, The prediction of transient heat transfer performance of thermal energy storage devices. Chem. Eng. Progress Symposium Ser. 61 (1965), 289-297.

[3] S. Agmon, On the eigenfunction and on the the eigenvalues of general boundary value problems. Comm. Pure Appl. Math. 15 (1962), 119-147. | Zbl | MR

[4] H. Amann, Parabolic evolution equations and nonlinear boundary conditions. J. Differential Equations 72 (1988), 201-269. | Zbl | MR

[5] M. Baerns - H. Hofmann - A. Renken, Chemische Reaktionstechnik. G. Thieme, Stuttgart, 1987.

[6] J. Bergh - J. Löfström, Interpolation Spaces. An Introduction. Springer, Berlin, 1976. | Zbl | MR

[7] A.P. Calderón, On an inverse boundary value problem. Seminar on Numerical Analysis and its Application to Coninuum Physics, Soc. Brasileira de Matemàtica, Rio de Janeiro (1980), 65-73. | MR

[8] R. Courant - D. Hilbert, Methoden der Mathematischen Physik II. Springer, Berlin, 1965. | MR

[9] J. Crank, The Mathematics of Diffusion. Clarendon Press, Oxford, 1975. | Zbl | MR

[10] J. Escher, Nonlinear elliptic systems with dynamic boundary conditions. Math. Z. 210 (1992), 413-439. | Zbl | MR

[11] J. Escher, On the qualitative behaviour of some semilinear parabolic problems. To appear in Differential Integral Equations. | Zbl | MR

[12] T. Hintermann, Evolution equations with dynamic boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 113 (1989), 43-60. | Zbl | MR

[13] R.E. Langer, A problem in diffusion or in the flow of heat for a solid in contact with a fluid. Tôhoku Math. J. 35 (1932), 260-275. | Zbl | JFM

[14] L. LAPIDUS - N.R. AMUNDSON (EDS.), Chemical Reactor Theory. Prentice-Hall, Englewood Cliffs, 1977. | MR

[15] J.-L. Lions, Quelques Méthodes de Résolution des Probèmes aux Limites Non Linéaires. Dunod, Paris, 1969. | Zbl | MR

[16] J.-L. Lions - E. Magenes, Problemi ai limiti non omogenei V. Ann. Scuola Norm. Sup. Pisa Cl. Sci. XVI (1962), 1-44. | Zbl | MR | Numdam

[17] J.-L. Lions - E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I. Springer, Berlin, Heidelberg -New York, 1972. | Zbl

[18] A Majda, The location of the spectrum of the dissipative acoustic operator. Indiana Univ. Math. J. 25 (1976), 973-987. | Zbl | MR

[19] H.W. March - W. Weaver, The diffusion problem for a solid in contact with a stirred liquid. Phys. Rev. 31 (1928), 1072-1082.

[20] A. Nachmann, Reconstruction from boundary measurements. Ann. of Math. 128 (1988), 531-576. | Zbl

[21] A. Nachmann - J. Sylvester - G. Uhlmann, An n-dimensional Borg-Levison theorem. Comm. Math. Phys. 115 (1988), 595-605. | Zbl | MR

[22] A. Pazy, Semigroups of Linear Operators and Application to Partial Differential Equations. Springer, Berlin- New York, 1983. | Zbl | MR

[23] B.E. Perterson, Introduction to Fourier Transform and Pseudo-Differential Operators. Pitman, Boston- London, 1983. | Zbl

[24] M.G. Slinko - K. Hartmann, Methoden und Programme zur Berechnung Chemischer Reaktoren. Akademie-Verlag, Berlin, 1972.

[25] P. Stefanov, Stability of the inverse problem in potential scattering at fixed energy. Ann. Inst. Fourier (Grenoble) 40 (1990), 867-884. | Zbl | MR | Numdam

[26] E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, 1970. | Zbl | MR

[27] H.B. Stewart, Generation of analytic semigroups by strongly elliptic operators under general boundary conditions. Trans. Amer. Math. Soc. 199 (1974), 141-162. | Zbl | MR

[28] H.B. Stewart, Generation of analytic semigroups by strongly elliptic operators. Trans. Amer. Math. Soc. 259 (1980), 299-310. | Zbl | MR

[29] J. Sylvester - G. Uhlmann, A uniqueness theorem for an inverse boundary value problem in electrical prospection. Comm. Pure Appl. Math. 39 (1986), 92-112. | Zbl | MR

[30] J. Sylvester - G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem. Ann. of Math. 125 (1987), 153-169. | Zbl | MR

[31] J. Sylvester - G. Uhlmann, Inverse boundary problem at the boundary - continuous dependence. Comm. Pure Appl. Math. 41 (1988), 197-221. | Zbl | MR

[32] H. Triebel, Interpolation Theory, Function spaces, Differential Operators. North-Holland, Amsterdam, 1978. | Zbl | MR

[33] H. Triebel, Theory of Function Spaces. Birkhäuser, Basel, 1983. | Zbl | MR

[34] H. Triebel, Theory of Function Spaces II. Birkhäuser, Basel, 1992. | Zbl | MR

[35] R.D. Vold - M.J. Vold, Colloid and Interface Chemistry. Addison-Wesley, Reading-Mass., 1983.