Compactness and non-compactness for Yamabe-type problems

Fernando Codá Marques

doi:10.1007/978-3-319-19902-3_9

Compactness and non-compactness for Yamabe-type problems

Fernando Codá Marques

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The Yamabe equation is one of the most natural and well-studied second-order semilinear elliptic equations arising in geometric variational problems. The existence theory is classical, while it follows from the works (Brendle, J Am Math Soc 21:951–979, 2008; Brendle and Marques, J Differ Geom 81:225–250, 2009) and (Khuri et al., J Differ Geom 81:143–196, 2009) that n = 25 is a critical dimension for compactness/noncompactness issues (or a priori estimates). In this survey article we review these results and discuss more recent related work on Yamabe-type problems.

Original language	English (US)
Pages (from-to)	121-131
Number of pages	11
Journal	Progress in Nonlinear Differential Equations and Their Application
Volume	86
DOIs	https://doi.org/10.1007/978-3-319-19902-3_9
State	Published - 2017

All Science Journal Classification (ASJC) codes

Analysis
Computational Mechanics
Mathematical Physics
Control and Optimization
Applied Mathematics

Keywords

Covariance
Manifold

Access to Document

10.1007/978-3-319-19902-3_9

Cite this

@article{ddc42b661df2403bb8ddd19ff8bf0473,

title = "Compactness and non-compactness for Yamabe-type problems",

abstract = "The Yamabe equation is one of the most natural and well-studied second-order semilinear elliptic equations arising in geometric variational problems. The existence theory is classical, while it follows from the works (Brendle, J Am Math Soc 21:951–979, 2008; Brendle and Marques, J Differ Geom 81:225–250, 2009) and (Khuri et al., J Differ Geom 81:143–196, 2009) that n = 25 is a critical dimension for compactness/noncompactness issues (or a priori estimates). In this survey article we review these results and discuss more recent related work on Yamabe-type problems.",

keywords = "Covariance, Manifold",

author = "Marques, \{Fernando Cod{\'a}\}",

note = "Publisher Copyright: {\textcopyright} 2015, Springer International Publishing Switzerland.",

year = "2017",

doi = "10.1007/978-3-319-19902-3\_9",

language = "English (US)",

volume = "86",

pages = "121--131",

journal = "Progress in Nonlinear Differential Equations and Their Application",

issn = "1421-1750",

publisher = "Springer US",

}

TY - JOUR

T1 - Compactness and non-compactness for Yamabe-type problems

AU - Marques, Fernando Codá

PY - 2017

Y1 - 2017

N2 - The Yamabe equation is one of the most natural and well-studied second-order semilinear elliptic equations arising in geometric variational problems. The existence theory is classical, while it follows from the works (Brendle, J Am Math Soc 21:951–979, 2008; Brendle and Marques, J Differ Geom 81:225–250, 2009) and (Khuri et al., J Differ Geom 81:143–196, 2009) that n = 25 is a critical dimension for compactness/noncompactness issues (or a priori estimates). In this survey article we review these results and discuss more recent related work on Yamabe-type problems.

AB - The Yamabe equation is one of the most natural and well-studied second-order semilinear elliptic equations arising in geometric variational problems. The existence theory is classical, while it follows from the works (Brendle, J Am Math Soc 21:951–979, 2008; Brendle and Marques, J Differ Geom 81:225–250, 2009) and (Khuri et al., J Differ Geom 81:143–196, 2009) that n = 25 is a critical dimension for compactness/noncompactness issues (or a priori estimates). In this survey article we review these results and discuss more recent related work on Yamabe-type problems.

KW - Covariance

KW - Manifold

UR - https://www.scopus.com/pages/publications/85035133273

UR - https://www.scopus.com/pages/publications/85035133273#tab=citedBy

U2 - 10.1007/978-3-319-19902-3_9

DO - 10.1007/978-3-319-19902-3_9

M3 - Article

AN - SCOPUS:85035133273

SN - 1421-1750

VL - 86

SP - 121

EP - 131

JO - Progress in Nonlinear Differential Equations and Their Application

JF - Progress in Nonlinear Differential Equations and Their Application

ER -

Compactness and non-compactness for Yamabe-type problems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this