The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.
The spectral radius is considered to be an asymptotic measure of convergence because it predicts the worst-case error reduction over many iterations. It can be shown [9, 20] that, in any vector norm, p(R) : llRmlll/mTherefore, ...
M. Anderson, Metrics of positive Ricci curvature with large diameter, Manus. Math. 68 (1990), 405–415. M. Anderson, Convergence and rigidity of manifolds under Ricci curvature bounds, Invent. Math. 102 (1990), 429–445.
[Da1971] R. Davies, Some remarks on the Kakeya problem, Proc. Cambridge Philos. Soc. 69 (1971), 417–421. [DaPuRo1961] M. Davis, H. Putnam, J. Robinson, The decision problem for exponential Diophantine equations, Ann. Math.
Partial Differential Equations: Foundations and integral representations
Bureau of Standards Report 1629 (1952). Hadamard, J. [1] Lectures on Cauchy's problem in linear partial differential equations, reprinted by Dover Publ., New York, 1952. Hellwig, G. [1] Partielle Differentialgleichungen, Teubner, ...
MR0341351 D. C. Robinson, Uniqueness of the Kerr black hole, Phys. Rev. Lett. 34 (1975), 905– 906. D. C. Robinson, A simple proof of the generalization of Israel's theorem, General Relativity and Gravitation 8 (August 1977), 695–698.
Partial Differential Equations
Pseudodifferential Operators
This text provides an introduction to the theory of partial differential equations.
This is the second edition of the now definitive text on partial differential equations (PDE).