Vy Khoi Le's Books

Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

By: Dang D. Ang,Rudolf Gorenflo,Vy K. Le,Dang D. Trong

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Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

By: Dang D. Ang,Rudolf Gorenflo,Vy K. Le,Dang D. Trong

Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations.

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Page Count

188

Publisher

Springer

Published Date

ISBN 10

3540456589

ISBN 13

9783540456582

Global Bifurcation in Variational Inequalities

Applications to Obstacle and Unilateral Problems

By: Vy Khoi Le,Klaus Schmitt

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Global Bifurcation in Variational Inequalities

Applications to Obstacle and Unilateral Problems

By: Vy Khoi Le,Klaus Schmitt

An up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems; equations from fluid mechanics and quasilinear elliptic partial differential equations. The tools employed are those of modern nonlinear analysis. Accessible to graduate students and researchers who work in nonlinear analysis, nonlinear partial differential equations, and additional research disciplines that use nonlinear mathematics.

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Page Count

261

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461218209

ISBN 13

9781461218203

Nonsmooth Variational Problems and Their Inequalities

Comparison Principles and Applications

By: Siegfried Carl,Vy Khoi Le,Dumitru Motreanu

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Nonsmooth Variational Problems and Their Inequalities

Comparison Principles and Applications

By: Siegfried Carl,Vy Khoi Le,Dumitru Motreanu

This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.

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Page Count

404

Publisher

Springer Science & Business Media

Published Date

ISBN 10

038746252X

ISBN 13

9780387462523

Multi-Valued Variational Inequalities and Inclusions

By: Siegfried Carl,Vy Khoi Le

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Multi-Valued Variational Inequalities and Inclusions

By: Siegfried Carl,Vy Khoi Le

This book focuses on a large class of multi-valued variational differential inequalities and inclusions of stationary and evolutionary types with constraints reflected by subdifferentials of convex functionals. Its main goal is to provide a systematic, unified, and relatively self-contained exposition of existence, comparison and enclosure principles, together with other qualitative properties of multi-valued variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents, and Beppo-Levi spaces. A general and comprehensive sub-supersolution method (lattice method) is developed for both stationary and evolutionary multi-valued variational inequalities, which preserves the characteristic features of the commonly known sub-supersolution method for single-valued, quasilinear elliptic and parabolic problems. This method provides a powerful tool for studying existence and enclosure properties of solutions when the coercivity of the problems under consideration fails. It can also be used to investigate qualitative properties such as the multiplicity and location of solutions or the existence of extremal solutions. This is the first in-depth treatise on the sub-supersolution (lattice) method for multi-valued variational inequalities without any variational structures, together with related topics. The choice of the included materials and their organization in the book also makes it useful and accessible to a large audience consisting of graduate students and researchers in various areas of Mathematical Analysis and Theoretical Physics.

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