**Author**: N.A

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**Category:**Differential equations

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# Search Results for: variational-principles-and-free-boundary-problems-pure-applied-mathematics-monograph

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Differential equations

**Page:** N.A

**View:** 8481

*Theory and Applications*

**Author**: Darya Apushkinskaya

**Publisher:** Springer

**ISBN:** 3319970798

**Category:**

**Page:** N.A

**View:** 9826

**Author**: Michael Bildhauer

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540402985

**Category:** Mathematics

**Page:** 217

**View:** 5639

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.

**Author**: James Terrence Kelly

**Publisher:** Nova Publishers

**ISBN:** 9781604561715

**Category:** Science

**Page:** 347

**View:** 9029

Applying mathematics to biology has a long history, but only recently has there been an explosion of interest in the field. Some reasons for this include: the explosion of data-rich information sets, due to the genomics revolution, which are difficult to understand without the use of analytical tools, recent development of mathematical tools such as chaos theory to help understand complex, non-linear mechanisms in biology, an increase in computing power which enables calculations and simulations to be performed that were not previously possible, and an increasing interest in in-silico experimentation due to the complications involved in human and animal research. This new book presents the latest leading-edge research in the field.
*Applications to Nonlinear PDEs and Fluid Mechanics*

**Author**: S.N. Antontsev,J.I. Diaz,S. Shmarev

**Publisher:** Springer Science & Business Media

**ISBN:** 1461200911

**Category:** Technology & Engineering

**Page:** 332

**View:** 3657

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.

**Author**: M. A. Lavrent’ev

**Publisher:** Courier Dover Publications

**ISBN:** 0486160289

**Category:** Mathematics

**Page:** 160

**View:** 3262

Famous monograph by a distinguished mathematician presents an innovative approach to classical boundary value problems. The treatment employs the basic scheme first suggested by Hilbert and developed by Tonnelli. 1963 edition.

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematical analysis

**Page:** N.A

**View:** 4225

*Seria Matematică, informatică*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematics

**Page:** N.A

**View:** 731

*Mathematica*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematics

**Page:** N.A

**View:** 3738

*Variational Methods and Existence Theorems*

**Author**: Christof Eck,Jiri Jarusek,Miroslav Krbec

**Publisher:** CRC Press

**ISBN:** 9781420027365

**Category:** Mathematics

**Page:** 398

**View:** 312

The mathematical analysis of contact problems, with or without friction, is an area where progress depends heavily on the integration of pure and applied mathematics. This book presents the state of the art in the mathematical analysis of unilateral contact problems with friction, along with a major part of the analysis of dynamic contact problems without friction. Much of this monograph emerged from the authors' research activities over the past 10 years and deals with an approach proven fruitful in many situations. Starting from thin estimates of possible solutions, this approach is based on an approximation of the problem and the proof of a moderate partial regularity of the solution to the approximate problem. This in turn makes use of the shift (or translation) technique - an important yet often overlooked tool for contact problems and other nonlinear problems with limited regularity. The authors pay careful attention to quantification and precise results to get optimal bounds in sufficient conditions for existence theorems. Unilateral Contact Problems: Variational Methods and Existence Theorems a valuable resource for scientists involved in the analysis of contact problems and for engineers working on the numerical approximation of contact problems. Self-contained and thoroughly up to date, it presents a complete collection of the available results and techniques for the analysis of unilateral contact problems and builds the background required for further research on more complex problems in this area.

**Author**: Jürgen Jost

**Publisher:** John Wiley & Sons Inc

**ISBN:** N.A

**Category:** Mathematics

**Page:** 236

**View:** 1303

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.

**Author**: Vesselin Petkov,Luchezar N. Stoyanov

**Publisher:** John Wiley & Sons Inc

**ISBN:** N.A

**Category:** Mathematics

**Page:** 313

**View:** 9602

**Author**: Harry Hochstadt

**Publisher:** Courier Corporation

**ISBN:** 0486168786

**Category:** Science

**Page:** 352

**View:** 5647

Comprehensive text provides a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation.

**Author**: Arshak Petrosyan,Henrik Shahgholian,Nina N. Ural'ceva

**Publisher:** American Mathematical Soc.

**ISBN:** 0821887947

**Category:** Mathematics

**Page:** 221

**View:** 2981

The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.

**Author**: Erich Zauderer

**Publisher:** John Wiley & Sons

**ISBN:** N.A

**Category:** Mathematics

**Page:** 779

**View:** 4856

An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

**Author**: Solomon G. Mikhlin

**Publisher:** Wiley

**ISBN:** N.A

**Category:** Mathematics

**Page:** 286

**View:** 9949

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.

**Author**: Luis Angel Caffarelli

**Publisher:** Edizioni della Normale

**ISBN:** 9788876422492

**Category:** Mathematics

**Page:** 54

**View:** 1428

The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.

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