Calculus Of Variations And Geometric Evolution Problems

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Calculus of Variations and Geometric Evolution Problems

F. Bethuel,G. Huisken,S. Mueller,K. Steffen
Calculus of Variations and Geometric Evolution Problems Book PDF

Author : F. Bethuel,G. Huisken,S. Mueller,K. Steffen
Publisher : Springer
Page : 299 pages
File Size : 52,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540488132

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Calculus of Variations and Geometric Evolution Problems by F. Bethuel,G. Huisken,S. Mueller,K. Steffen Pdf

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

Calculus of Variations and Partial Differential Equations

Luigi Ambrosio,Norman Dancer
Calculus of Variations and Partial Differential Equations Book PDF

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642571862

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Calculus of Variations and Partial Differential Equations by Luigi Ambrosio,Norman Dancer Pdf

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Calculus of Variations and Geometric Evolution Problems

F. Bethuel,G. Huisken,S. Mueller,K. Steffen
Calculus of Variations and Geometric Evolution Problems Book PDF

Author : F. Bethuel,G. Huisken,S. Mueller,K. Steffen
Publisher : Springer
Page : 298 pages
File Size : 43,7 Mb
Release : 1999-10-19
Category : Mathematics
ISBN : 3540659773

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Calculus of Variations and Geometric Evolution Problems by F. Bethuel,G. Huisken,S. Mueller,K. Steffen Pdf

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

Calculus of Variations and Partial Differential Equations

Luigi Ambrosio,Norman Dancer
Calculus of Variations and Partial Differential Equations Book PDF

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 51,8 Mb
Release : 2000-01-24
Category : Mathematics
ISBN : 3540648038

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Calculus of Variations and Partial Differential Equations by Luigi Ambrosio,Norman Dancer Pdf

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Calculus of Variations I

Mariano Giaquinta,Stefan Hildebrandt
Calculus of Variations I Book PDF

Author : Mariano Giaquinta,Stefan Hildebrandt
Publisher : Springer Science & Business Media
Page : 512 pages
File Size : 48,5 Mb
Release : 2004-06-23
Category : Mathematics
ISBN : 354050625X

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Calculus of Variations I by Mariano Giaquinta,Stefan Hildebrandt Pdf

This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems—such as those of geometric optics—of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.

Differential Geometry, Calculus of Variations, and Their Applications

George M. Rassias,Themistocles M. Rassias
Differential Geometry Calculus of Variations and Their Applications Book PDF

Author : George M. Rassias,Themistocles M. Rassias
Publisher : CRC Press
Page : 550 pages
File Size : 44,8 Mb
Release : 2023-05-31
Category : Mathematics
ISBN : 9781000950724

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Differential Geometry, Calculus of Variations, and Their Applications by George M. Rassias,Themistocles M. Rassias Pdf

This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.

Variational Problems in Riemannian Geometry

Paul Baird,Ahmad El Soufi,Ali Fardoun,Rachid Regbaoui
Variational Problems in Riemannian Geometry Book PDF

Author : Paul Baird,Ahmad El Soufi,Ali Fardoun,Rachid Regbaoui
Publisher : Birkhäuser
Page : 158 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879682

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Variational Problems in Riemannian Geometry by Paul Baird,Ahmad El Soufi,Ali Fardoun,Rachid Regbaoui Pdf

This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.

Geometric Measure Theory and the Calculus of Variations

William K. Allard,Frederick J. Almgren
Geometric Measure Theory and the Calculus of Variations Book PDF

Author : William K. Allard,Frederick J. Almgren
Publisher : American Mathematical Soc.
Page : 484 pages
File Size : 52,8 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 0821868071

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Geometric Measure Theory and the Calculus of Variations by William K. Allard,Frederick J. Almgren Pdf

These twenty-six papers survey a cross section of current work in modern geometric measure theory and its applications in the calculus of variations. Presently the field consists of a jumble of new ideas, techniques and intuitive hunches; an exchange of information has been hindered, however, by the characteristic length and complexity of formal research papers in higher-dimensional geometric analysis. This volume provides an easier access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field. The papers are aimed at analysts and geometers who may use geometric measure-theoretic techniques, and they require a mathematical sophistication at the level of a second year graduate student. The papers included were presented at the 1984 AMS Summer Research Institute held at Humboldt State University. A major theme of this institute was the introduction and application of multiple-valued function techniques as a basic new tool in geometric analysis, highlighted by Almgren's fundamental paper Deformations and multiple-valued functions. Major new results discussed at the conference included the following: Allard's integrality and regularity theorems for surfaces stationary with respect to general elliptic integrands; Scheffer's first example of a singular solution to the Navier-Stokes equations for a fluid flow with opposing force; and Hutchinson's new definition of the second fundamental form of a general varifold.

The Shape of Things

Shawn W. Walker
The Shape of Things Book PDF

Author : Shawn W. Walker
Publisher : SIAM
Page : 156 pages
File Size : 48,7 Mb
Release : 2015-12-17
Category : Mathematics
ISBN : 9781611973952

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The Shape of Things by Shawn W. Walker Pdf

Many things around us have properties that depend on their shape?for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a ?shape variable.? This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.

Inverse Problems and Imaging

Luis L. Bonilla
Inverse Problems and Imaging Book PDF

Author : Luis L. Bonilla
Publisher : Springer
Page : 200 pages
File Size : 45,6 Mb
Release : 2009-06-19
Category : Mathematics
ISBN : 9783540785477

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Inverse Problems and Imaging by Luis L. Bonilla Pdf

Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics.

Multiscale Problems in the Life Sciences

Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz
Multiscale Problems in the Life Sciences Book PDF

Author : Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz
Publisher : Springer
Page : 330 pages
File Size : 42,7 Mb
Release : 2008-04-08
Category : Mathematics
ISBN : 9783540783626

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Multiscale Problems in the Life Sciences by Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz Pdf

The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to biology and medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory, and game theory.

Stochastic Geometry

W. Weil,A. Baddeley,I. Bárány,R. Schneider
Stochastic Geometry Book PDF

Author : W. Weil,A. Baddeley,I. Bárány,R. Schneider
Publisher : Springer
Page : 292 pages
File Size : 54,7 Mb
Release : 2006-10-26
Category : Mathematics
ISBN : 9783540381754

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Stochastic Geometry by W. Weil,A. Baddeley,I. Bárány,R. Schneider Pdf

Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.

Geometric Analysis and PDEs

Matthew J. Gursky,Ermanno Lanconelli,Andrea Malchiodi,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang
Geometric Analysis and PDEs Book PDF

Author : Matthew J. Gursky,Ermanno Lanconelli,Andrea Malchiodi,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang
Publisher : Springer
Page : 256 pages
File Size : 42,8 Mb
Release : 2009-07-31
Category : Mathematics
ISBN : 9783642016745

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Geometric Analysis and PDEs by Matthew J. Gursky,Ermanno Lanconelli,Andrea Malchiodi,Gabriella Tarantello,Xu-Jia Wang,Paul C. Yang Pdf

This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

Enumerative Invariants in Algebraic Geometry and String Theory

Marcos Marino,Michael Thaddeus,Ravi Vakil
Enumerative Invariants in Algebraic Geometry and String Theory Book PDF

Author : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 50,8 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783540798132

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Enumerative Invariants in Algebraic Geometry and String Theory by Marcos Marino,Michael Thaddeus,Ravi Vakil Pdf

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

Measure Theory and Nonlinear Evolution Equations

Flavia Smarrazzo,Alberto Tesei
Measure Theory and Nonlinear Evolution Equations Book PDF

Author : Flavia Smarrazzo,Alberto Tesei
Publisher : Walter de Gruyter GmbH & Co KG
Page : 456 pages
File Size : 40,8 Mb
Release : 2022-04-19
Category : Mathematics
ISBN : 9783110556902

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Measure Theory and Nonlinear Evolution Equations by Flavia Smarrazzo,Alberto Tesei Pdf

This carefully written text on measure theory with applications to partial differential equations covers general measure theory, Lebesgue spaces of real-valued and vector-valued functions, different notions of measurability for the latter, weak convergence of functions and measures, Radon and Young measures, capacity, and finally applications to quasilinear parabolic problems (in particular, forward-backward equations).