Motivated by the study of self-gravitating cosmic strings, we pursue the well-known method by Bandle to obtain a weak version of the classical Alexandrov’s isoperimetric inequality. In fact, we derive some quantitative estimates for weak subsolutions of a Liouville-type equation with conical singularities. Actually, we succeed in generalizing previously known results, including Bol’s inequality and pointwise estimates, to the case where the solutions solve the equation just in the sense of distributions. Next, we derive some new pointwise estimates suitable to be applied to a class of singular cosmic string equations. Finally, interestingly enough, we apply these results to establish a minimal mass property for solutions of the cosmic string equation which are supersolutions of the singular Liouville-type equation.

Bartolucci, D., Castorina, D. (2016). Self-gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 18(4) [10.1142/S0219199715500686].

Self-gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations

D. Bartolucci;
2016-08-01

Abstract

Motivated by the study of self-gravitating cosmic strings, we pursue the well-known method by Bandle to obtain a weak version of the classical Alexandrov’s isoperimetric inequality. In fact, we derive some quantitative estimates for weak subsolutions of a Liouville-type equation with conical singularities. Actually, we succeed in generalizing previously known results, including Bol’s inequality and pointwise estimates, to the case where the solutions solve the equation just in the sense of distributions. Next, we derive some new pointwise estimates suitable to be applied to a class of singular cosmic string equations. Finally, interestingly enough, we apply these results to establish a minimal mass property for solutions of the cosmic string equation which are supersolutions of the singular Liouville-type equation.
ago-2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Self-gravitating cosmic strings; isoperimetric inequalities on surfaces; singular Liouville equations; conical singularities.
supported by MIUR project Metodi Variazionali ed Equazioni Differenziali nonlineari.
Bartolucci, D., Castorina, D. (2016). Self-gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 18(4) [10.1142/S0219199715500686].
Bartolucci, D; Castorina, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/204605
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