A new rearrangement inequality and its application for -constraint minimizing problems

作者：Shibata Masataka^*

来源：Mathematische Zeitschrift, 2017, 287(1-2): 341-359.

DOI：10.1007/s00209-016-1828-1

• Rearrangement inequalities
• Minimizing sequences
• Nonlinear Schrodinger equations

In this paper, we introduce a new type rearrangement inequality based on the Steiner rearrangement. To show orbital stability of standing wave solutions with respect to a nonlinear Schrodinger equation, -precompactness of minimizing sequence of -constraint minimizing problem is very important. Usually, by using the concentration compactness principle and some scaling argument, -precompactness is obtained. To prove -precompactness without scaling arguments, we introduce the rearrangement. The Steiner rearrangement is defined as a map from to , whereas our rearrangement is defined as a map from to . By using the rearrangement, we show a strict inequality under simple assumptions.

• 出版日期2017-10