Воронеж: Воронежский государственный университет, 2021. — 95 с. Учебное пособие подготовлено на кафедре математического анализа математического факультета Воронежского государственного университета. Рекомендовано для студентов и аспирантов математического факультета, а также для специалистов. Для направлений: 01.04.01 ‒ Математика, 02.04.01 ‒ Математика и компьютерные науки...
Springer, 2025. — 154 p. This textbook introduces variational calculus and regularization methods for inverse problems, seamlessly blending classical concepts with contemporary computational applications, particularly in the field of image processing. The classical perspective draws upon foundational topics explored by pioneers such as Euler and Lagrange, establishing a solid...
Springer, 2024. — 444 p. This book is about the theory of so-called Schwarz methods for solving variational problems in a Hilbert space V arising from linear equations and their associated quadratic minimization problems. Schwarz methods are based on the construction of a sequence of approximate solutions by solving auxiliary variational problems on a set of (smaller,...
Princeton University Press, 1989. — 158 p. This book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is...
Laxmi Publications, 2006. — 206 p. Curves in Space Surfaces in Space Variational Problems withFixed Boundaries Variational Problems with Moving Boundaries Sufficient Conditions for an Extremum
Berlin: de Gruyter, 2020. — 602 p. The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and...
Oxford: Oxford University Press, 1995. — 245 p. A paperback edition of this successful textbook for final year undergraduate mathematicians and control engineering students, this book contains exercises and many worked examples, with complete solutions and hints making it ideal not only as a class textbook but also for individual study. The intorduction to optimal control...
Berlin: Springer, 1998. — 298 p. Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations,...
Oxford University Press, 2002. — 229 p. The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing to Fracture Mechanics. This text, written by an expert...
De Gruyter, 1997. — 300 p. Constrained minimization Preliminaries Constrained minimization Dual method Minimizers with the least energy Application of dual method Multiple solutions of nonhomogeneous equation Sets of constraints Constrained minimization for Ff Subcritical problem Application to the p-Laplacian Critical problem Bibliographical notes Applications of...
New York: Nova Science Publishers, 2018. — 314 p. This book encompasses recent developments of variational calculus for time scales. It is intended for use in the field of variational calculus and dynamic calculus for time scales. It is also suitable for graduate courses in the above fields. This book contains eight chapters, and these chapters are pedagogically organized. This...
Cham: Springer, 2022. — 284 p. This book provides a comprehensive introduction to the Calculus of Variations and its use in modelling mechanics and physics problems. Presenting a geometric approach to the subject, it progressively guides the reader through this very active branch of mathematics, accompanying key statements with a huge variety of exercises, some of them solved....
Cham: Springer, 2021. — 223 p. This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions...
New York: Pitman Publishing, 1982. — 332 p. Generalities Notations Classical methods: characteristics Optimal Control theory The vanishing viscosity method Viscosity solutions: uniqueness and stability Accretivity of the Hamilton-Jacobi operator The Dirichlet Problem The main existence result The case when \Omega is bounded and smooth, and H is superquadratic The general case...
Cambridge: Cambridge University Press, 2010. — 386 p. This comprehensive introduction to the calculus of variations and its main principles also presents their real-life applications in various contexts: mathematical physics, differential geometry, and optimization in economics. Based on the authors' original work, it provides an overview of the field, with examples and...
Cambridge: Cambridge Scholars Publishing, 2019. — 187 p. This book focuses on the calculus of variations and related applications which combine tools and methods from partial differential equations with geometrical techniques. More precisely, it is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of...
New York: Springer, 2007. — 402 p. This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as is multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. The main purpose of this book is to provide a...
New York: Springer, 2019. — 135 p. The Variable-Order Fractional Calculus of Variations is devoted to the study of fractional operators with variable order and, in particular, variational problems involving variable-order operators. This brief presents a new numerical tool for the solution of differential equations involving Caputo derivatives of fractional variable order....
New York: Springer, 1981. — 313 p. When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching...
Cambridge: Cambridge University Press, 2016. — 400 p.
This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their...
Boca Raton: CRC Press, 2013. — 236 p.
The purpose of the calculus of variations is to find optimal solutions to engineering problems whose optimum may be a certain quantity, shape, or function. Applied Calculus of Variations for Engineers addresses this important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it...
New York: Chapman and Hall/CRC, 1993. - 110p.
This monograph is unique in its treatment of the application of methods of nonstandard analysis to the theory of curves in the calculus of variations. It will be of particular value to researchers in the calculus of variations and optimal control theory.
Boca Raton: CRC Press, 2013. - 562p.
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient...
N.-Y.: Springer, 2013. - 606p.
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading...