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EXTENSION OF SOLUTIONS OF DIFFERENTIAL EQUATIONS

Leon Ehrenpreis

in The Universality of the Radon Transform

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198509783
eISBN:
9780191709166
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509783.003.0009
Subject:
Mathematics, Mathematical Physics

This chapter shows how the book's main theory allows for the treatment of extension problems for partial differential equations. The culmination of this is a solution of the asymptotic edge of the ... More


Complex manifolds

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0017
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This chapter examines complex manifolds. It discusses some basics concerning holomorphic functions on ℂn; the definition of a complex manifold; first examples of complex manifolds; the ... More


On Div-Curl for Higher Order

Loredana Lanzani and Andrew S. Raich

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0011
Subject:
Mathematics, Numerical Analysis

This chapter produces a new class of differential operators of order k (where k is any given positive integer) that satisfy an appropriate analogue of a Gagliardo–Nirenberg inequality for functions ... More


Sobolev Spaces Wk,p(Ω); A Resolution of the Dirichlet Principle

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 2: Contemporary Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733157
eISBN:
9780191797729
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733157.003.0015
Subject:
Mathematics, Analysis

This chapter introduces the Sobolev spaces of integer order on domains and discusses their embeddings and trace theorems. Here, the starting point is establishing various approximation results by ... More


Morrey and Campanato vs. Hardy and John-Nirenberg Spaces

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 2: Contemporary Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733157
eISBN:
9780191797729
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733157.003.0018
Subject:
Mathematics, Analysis

This chapter presents an analysis of decay rates of integral means of functions. It also provides an introduction of Morrey and Campanato spaces and their relation to Holder spaces. It also provides ... More


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