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Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.001.0001
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Wavelets have become a powerful tool in several applications by now. Their use for the numerical solution of operator equations has been investigated more recently. By now the theoretical ... More


Stochastic Homogenization and Energy of Infinite Sets of Points

Xavier Blanc

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0004
Subject:
Mathematics, Probability / Statistics, Analysis

This chapter presents, in a synthetic way, a series of recent works by X. Blanc, C. Le Bris, and P-L. Lions on homogenization of an elliptic partial differential equation under certain periodic or ... More


Transport-Elliptic Estimates

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0027
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter solves the underdetermined, elliptic equation ∂ⱼQsuperscript jl = Usuperscript l and Qsuperscript jl = Qsuperscript lj (Equation 1069) in order to eliminate the error term in the ... More


Nonlinear Elliptic Equations

Rüdiger Verfürth

in A Posteriori Error Estimation Techniques for Finite Element Methods

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199679423
eISBN:
9780191758485
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199679423.003.0005
Subject:
Mathematics, Applied Mathematics, Numerical Analysis

We present a posteriori error estimates for nonlinear stationary problems departing from an abstract result which establishes the basic equivalence of error and residual. The main tool is the ... More


A Posteriori Error Estimation Techniques for Finite Element Methods

Rüdiger Verfürth

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199679423
eISBN:
9780191758485
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199679423.001.0001
Subject:
Mathematics, Applied Mathematics, Numerical Analysis

Self-adaptive discretization methods nowadays are an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to ... More


Maximum Principles and Uniqueness Theorems

Charles L. Epstein and Rafe1 Mazzeo

in Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157122
eISBN:
9781400846108
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157122.003.0003
Subject:
Mathematics, Probability / Statistics

This chapter proves maximum principles for two parabolic and elliptic equations from which the uniqueness results follow easily. It also considers the main consequences of the maximum principle, both ... More


The dimensions of time

George Jaroszkiewicz

in Images of Time: Mind, Science, Reality

Published in print:
2016
Published Online:
January 2016
ISBN:
9780198718062
eISBN:
9780191787553
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198718062.003.0012
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the mathematical reasons why time has one dimension rather than two or more dimensions. It examines the flow of information, through a spacetime with a given signature, in ... More


The Calder´on-Zygmund Theory II: Maximal Hypoellipticity

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0002
Subject:
Mathematics, Analysis

This chapter remains in the single-parameter case and turns to the case when the metric is a Carnot–Carathéodory (or sub-Riemannian) metric. It defines a class of singular integral operators adapted ... More


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