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Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: A survey

Autor
Cabre, X.
Tipus d'activitat
Article en revista
Revista
Chinese annals of mathematics. Series B
Data de publicació
2017-01-05
Volum
38
Número
1
Pàgina inicial
201
Pàgina final
214
DOI
https://doi.org/10.1007/s11401-016-1067-0 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/100681 Obrir en finestra nova
URL
http://link.springer.com/article/10.1007%2Fs11401-016-1067-0 Obrir en finestra nova
Resum
This paper presents the proof of several inequalities by using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP estimate. First, the author gives a new and simple proof of a lower bound of Berestycki, Nirenberg, and Varadhan concerning the principal eigenvalue of an elliptic operator with bounded measurable coefficients. The rest of the paper is a survey on the proofs of several isoperimetric and Sobolev inequalities using the ABP technique. This includes new p...
Citació
Cabre, X. Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: A survey. "Chinese annals of mathematics. Series B", 5 Gener 2017, vol. 38, núm. 1, p. 201-214.
Paraules clau
ABP estimate, Isoperimetric inequalities, Principal eigenvalue, Wulff shapes
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

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