Self gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations
Self gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations
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DOI：
10.1142/s0219199715500686
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发表时间：
2014-09
期刊：
影响因子：
--
通讯作者：
D. Bartolucci;D. Castorina
中科院分区：
文献类型：
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作者：
D. Bartolucci;D. Castorina
受自引力宇宙弦研究的启发，我们采用了C。Bandle得到了经典Alexandrov等周不等式的一个弱形式。事实上，我们得到了一些定量估计的弱子解的刘维型方程的锥奇。实际上，我们成功地推广以前已知的结果，包括波尔的不等式和逐点估计的情况下，解决方案解决方程只是在意义上的分布。接下来，我们得到了一些适合于应用于一类奇异宇宙弦方程的\uv{new}逐点估计。最后，有趣的是，我们应用这些结果来建立一个最小的质量属性的宇宙弦方程的解决方案是\uv{supersolutions}的奇异刘维尔型方程。
Motivated by the study of self gravitating cosmic strings, we pursue the well known method by C. 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 \uv{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 \uv{supersolutions} of the singular Liouville-type equation.