Partial Differential Equations and Spectral Theory

ISBN-13: 9783034800235 / Angielski / Twarda / 2011 / 341 str.

Michael Demuth; Bert-Wolfgang Schulze; Ingo Witt

Opis

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

Spis treści

Preface.- L. Chen, M. Dreher: Quantum semiconductor models.- H. Bel Hadj Ali, A. Ben Amor, J. Brasche: Large coupling convergence: Overview and new results.- M. Ben-Artzi: Smooth spectral calculus.- W. Bauer, K. Furutani, C. Iwasaki: Spectral analysis and geometry of sub-Laplacian and related Grushin-type operators.- G. Mendoza: Zeta functions of elliptic cone operators.- P. McKeag, Y. Safarov: Pseudodifferential operators on manifolds: A coordinate-free approach.

O autorze

Bert-Wolfgang Schulze ist emeritierter Professor am Institut für Mathematik an der Universität Potsdam, Deutschland. Vor der politischen Wende war er Professor am Karl-Weierstrass-Institut in Berlin, 1984 Euler-Medaille der Akademie der Wisenschaften in Berlin. 1992-96 war er Leiter der Max-Planck-Arbeitsgruppe 'Partielle Differentialgleichungen und Komplexe Analysis' in Potsdam. Nach anfänglichem Studium in Geophysik erhielt er sein Universitätsdiplom in Mathematik in Leipzig 1968. Die Promotion zum Dr. rer.nat. 1970 und die Habilitation in Mathematik 1974 erfolgten an der Universität Rostock. Seine wissenschaftlichen Aktivitäten umfassen Potentialtheorie, Randwert-Probleme, pseudo-differentielle Algebren und Index-Theorie auf berandeten Mannigfaltgikeiten und Räumen mit Singularitäten, darunterTransmissions- und Riss Probleme, Asymptotik von Lösungen, Randwert-Theorie mit globalen Projektionsbedingungen.

Blurb

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear, expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

Contributors:

W. Bauer

H. BelHadjAli

A. Ben Amor

M. Ben-Artzi

J.F. Brasche

L. Chen

M. Dreher

K. Furutani

C. Iwasaki

P. McKeag

G.A. Mendoza

Y. Safarov