Convex Variational Problems with Linear, Nearly Linear And/or Anisotropic Growth Conditions


Author: Michael Bildhauer
Publisher: Springer Science & Business Media
ISBN: 9783540402985
Category: Mathematics
Page: 217
View: 9014

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The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.

Stability Criteria for Fluid Flows


Author: Adelina Georgescu,Lidia Palese
Publisher: World Scientific
ISBN: 9814289566
Category: Science
Page: 399
View: 9799

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This is a comprehensive and self-contained introduction to the mathematical problems of thermal convection. The book delineates the main ideas leading to the authors' variant of the energy method. These can be also applied to other variants of the energy method. The importance of the book lies in its focussing on the best concrete results known in the domain of fluid flows stability and in the systematic treatment of mathematical instruments used in order to reach them.

Two-dimensional geometric variational problems


Author: Jürgen Jost
Publisher: John Wiley & Sons Inc
ISBN: N.A
Category: Mathematics
Page: 236
View: 7428

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This monograph treats variational problems for mappings from a surface equipped with a conformal structure into Euclidean space or a Riemannian manifold. Presents a general theory of such variational problems, proving existence and regularity theorems with particular conceptual emphasis on the geometric aspects of the theory and thorough investigation of the connections with complex analysis. Among the topics covered are: Plateau's problem, the regularity theory of solutions, a variational approach for obtaining various conformal representation theorems, a general existence theorem for harmonic mappings, and a new approach to Teichmuller theory via harmonic maps.

Fourier series, transforms, and boundary value problems


Author: J. Ray Hanna,John H. Rowland
Publisher: Wiley-Interscience
ISBN: N.A
Category: Mathematics
Page: 354
View: 6859

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Retains both the spirit and philosophy of the popular First Edition. The primary changes consist of the addition of new material on integral transforms, discrete and fast Fourier transforms, series solutions, harmonic analysis, spherical harmonics and a glance at some of the numerical techniques for the solution of boundary value problems. With more than enough material for a one-semester course, it offers a full presentation of basic principles, and advanced topics are covered in the largely self-contained closing chapters. The order of presentation of some of the material has been rearranged to provide more flexibility in arranging courses.

Error Analysis in Numerical Processes


Author: Solomon G. Mikhlin
Publisher: Wiley
ISBN: N.A
Category: Mathematics
Page: 286
View: 2938

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Extends the traditional classification of errors so that the error of the method (truncation error) and the numerical error are subdivided into four classes: the approximation, the perturbation, the algorithm and the rounding error. This new subdivision of errors results in error estimates for a number of linear and nonlinear problems in numerical analysis. Obtained here are new results--errors in the conjugate direction method--as well as known results, such as errors in Gaussian elimination. Also presented are a posteriori error estimates, such as those derived for, and often by means of, the computed approximate solution.

Energy Methods for Free Boundary Problems

Applications to Nonlinear PDEs and Fluid Mechanics
Author: Stanislav Nikolaevich Antont︠s︡ev,J. I. Díaz,S. I. Shmarev
Publisher: Birkhauser
ISBN: N.A
Category: Mathematics
Page: 329
View: 9582

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