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

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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

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

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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.",

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year = "2017",

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AU - Marques, Fernando Codá

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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

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

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VL - 86

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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

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