Global Solutions in R2 for Three-Well Potential

• Main Authors: I-KUN, CHEN, 陳逸昆
• Other Authors: Chiun-Chuan Chen
• Format: Others
• Language: en_US
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/06089066119796731124

碩士 === 國立臺灣大學 === 數學研究所 === 89 === In this paper, we study the vector-valued problem in R2 -Laplation U + DW(U)=0 where W is a symmetric potential with three wells of equal depth. We show the existence of nontrivial smooth solution with 3n-layers. By a proper conformal mapping, the equation is transferred to the following equation. -Laplation U + r^(-l)DW(U)=0 l = 2(n-1)/n By the symmetry of 3n-layer solution, we can find a nontrivial smooth solution with three layers over R2/{o}.