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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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