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Gamma-Convergence for Beginners

Andrea Braides

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.001.0001
Subject:
Mathematics, Applied Mathematics

This book introduces the main concepts of the theory of De Giorgi's Gamma-convergence and gives a description of its main applications to the study of asymptotic variational problems. The content is ... More


Nonconforming finite element methods

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonconforming FEMs avoid the strong restrictions of conforming FEMs. So discontinuous ansatz and test functions, approximate test integrals, and strong forms are admitted. This allows the proof of ... More


Functional Analysis and Abstract Error Estimates

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0002
Subject:
Mathematics, Numerical Analysis

This chapter presents the basic functional analysis and abstract error estimates used in the book. A summary of the relevant theory of linear variational problems, compactness, and the Fredholm ... More


Forcing equivalence between kissing cylinders

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter formulates and proves the jump mechanism. It constructs a variational problem which proves forcing equivalence for the original Hamiltonian using Definition 6.18. It first constructs a ... More


Sobolev Spaces, Vector Function Spaces and Regularity

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0003
Subject:
Mathematics, Numerical Analysis

This chapter presents the basic functional analysis and abstract error estimates used in the book. A summary of the relevant theory of linear variational problems,compactness, and the Fredholm ... More


Boundary Value Problems in Dimensions 7, 4 and 3 Related to Exceptional Holonomy

Simon Donaldson

in Geometry and Physics: Volume I: A Festschrift in honour of Nigel Hitchin

Published in print:
2018
Published Online:
December 2018
ISBN:
9780198802013
eISBN:
9780191840500
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802013.003.0006
Subject:
Mathematics, Geometry / Topology

The variational point of view on exceptional structures in dimensions 6, 7 and 8 is one of Nigel Hitchin’s seminal contributions. One feature of this point of view is that it motivates the study of ... More


Variational formulation of boundary-value problems

Lallit Anand and Sanjay Govindjee

in Continuum Mechanics of Solids

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198864721
eISBN:
9780191896767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198864721.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses a variational formulation of boundary value problems in small deformation solid mechanics. It begins by introducing the important principle of virtual power, and shows that it ... More


The action functional and the harmonic oscillator

Jean-Michel Bismut

in Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691151298
eISBN:
9781400840571
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151298.003.0011
Subject:
Mathematics, Geometry / Topology

This chapter solves explicitly certain natural variational problems associated with a scalar hypoelliptic Laplacian, in the case where the underlying Riemannian manifold is an Euclidean vector space. ... More


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