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Birkhäuser - Birkhäuser Mathematics | Selected Works of Jindřich Nečas - PDEs, Continuum Mechanics and Regularity

Selected Works of Jindřich Nečas

PDEs, Continuum Mechanics and Regularity

Nečasová, Šárka, Pokorný, Milan, Sverak, Vladimir (Eds.)

2015, XIV, 781 p. 49 illus., 17 illus. in color.

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  • About this book

  • First time that J. Nečas’ important results have been collected in one publication
  • Some of the articles are not anymore available elsewhere
  • The theory of the PDEs of continuum mechanics is perhaps even more popular today than it was when Nečas’s seminal contributions to this area were written
The book collects the most significant contributions of the outstanding Czech mathematician Jindřich Nečas, who was honoured with the Order of Merit of the Czech Republic by President Václav Havel. Starting with Nečas’s brief biography and short comments on his role in the beginnings of modern PDE research in Prague, the book then follows the periods of his research career. The first part is devoted to the linear theory of partial differential equations. Its topics include the variational approach to linear boundary value problems and the Rellich - Nečas inequalities, together with their applications to boundary regularity. The second part is concerned with the regularity for nonlinear elliptic systems, which are related to Hilbert’s 19th and 20th problems. The third part focuses on Nonlinear Functional Analysis and its applications to non-linear PDEs, while the last part deals with topics in the mathematical theory of various models in Continuum Mechanics, including elasticity and plasticity, the Navier-Stokes equations, transonic flows, and multipolar fluids.
The editorial contributions were written by: I. Babuška, P. Ciarlet, P. Drábek, M. Feistauer, I. Hlaváček, J. Jarušek, O. John, J. Kristensen, A. Kufner, J. Málek, G. Mingione, Š. Nečasová, M. Pokorný, P. Quittner, T. Roubíček, G. Seregin and J. Stará.

Content Level » Research

Keywords » Navier-Stokes equations - calculus of variations - elliptic equations - fluid mechanics - non-linear functional analysis - regularity theory - solid mechanics - thermoelasticity

Related subjects » Birkhäuser Mathematics - Birkhäuser Physics

Table of contents 

1 Introduction.- 2 Short Biography of J. Nečas.- 3 Complete List of Nečas’ works.- 4 J. Nečas in the early 1960s.- 5 J. Nečas and the Prague School of PDE.- 6 Linear Elliptic Operators.- 7.1 Regularity for Non-linear Equations and Systems.- 7.2 Contribution of Mingione and Kristensen.- 8. Non-linear Functional Analysis, Calculus of Variations.- 9. Solid Mechanics, Elasticity, Thermoelasticity, and Plasticity.- 9.1 Mechanics of Solids.- 9.2 The Contribution of Jindřich Nečas to the Development of the Theory of Solvability of Contact Problems.- 10 Fluid Mechanics.- 11 Comments and Recollections by Collaborators and Students.- 12 Some Notable Personal Correspondence.- 13 Photographs.

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