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Dieses zweibändige Lehrbuch stellt das Gesamtgebiet der partiellen Differentialgleichungen - vom elliptischen,parabolischen und hyperbolischen Typ - in zwei und mehreren Veränderlichen vor. Im vorliegenden zweiten Band werden folgende Themen behandelt: Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, Schaudersche Theorie linearer elliptischer Differentialgleichungen, schwache Lösungen elliptischer Differentialgleichungen, nichtlineare partielle Differentialgleichungen und Charakteristikentheorie, nichtlineare elliptische Systeme mit differentialgeometrischen Anwendungen. Während im vorausgehenden Band die partiellen Differentialgleichungen mit Integraldarstellungen im Mittelpunkt standen, werden nun funktionalanalytische Lösungsmethoden vorgestellt. Dieses Lehrbuch kann daher für einen mehrsemestrigen Kurs verwendet werden. Fortgeschrittene Leser können jedes Kapitel auch unabhängig voneinander studieren.

Partial differential equations. --- Partial Differential Equations.

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The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of Lp Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, an extension of complex interpolation theory, and Navier-Stokes equations with small viscosity. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted. (SIAM Review, June 1998)

Partial differential equations --- differentiaalvergelijkingen

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The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, the space of pseudodifferential operators of harmonic oscillator type, and an index formula for elliptic systems of such operators. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.  (SIAM Review, June 1998)

Partial differential equations --- differentiaalvergelijkingen

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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

Partial differential equations --- differentiaalvergelijkingen

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This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations are given. The book contains an introduction to the Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, and functional analysis. The authors have succeeded admirably in bringing together a wealth of recent material, much of which appears in book form for the first time. This authoritative work is likely to become a standard reference on both the Laplace transform and its applications to the abstract Cauchy problem. ¦ The book is an excellent textbook as well. Proofs are always transparent and complete, and many topics that could have been considered as background material are covered as well. All this makes the text very accessible and self-contained. Applications to concrete differential operators are given throughout the text. Each chapter ends with historical and bibliographical comments. ¦ In summary, this book will be of interest to a wide audience of (functional) analysts and it should have a place in every mathematics library. Warmly recommended! Jan van Neerven, Nieuw Archief voor Wiskunde, No. 3, 2003

Partial differential equations --- differentiaalvergelijkingen