Constraint minimizers of inhomogeneous mass subcritical minimization problems

作者：Gao, Yongshuai; Li, Shuai^*

来源：MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44(13): 10062-10075.

DOI：10.1002/mma.7390

• inhomogeneous
• mass concentration
• mass subcritical
• minimizers

This paper considers minimizers of the following inhomogeneous L-2-subcritical energy functional @@@ E(u):= integral(RN) vertical bar del vertical bar(2)dx - 1/p +1 integral(RN) m(x)vertical bar u vertical bar(p+1)dx, @@@ under the mass constraint parallel to u parallel to(2)(2) = M. Here, N >= 1, p is an element of(1,1+4/N), M > 0 and the inhomogeneous term m(x) satisfies 0 < m(x) <= 1. Applying the concentration-compactness principle, we prove that this minimization problem admits minimizers for any M is an element of (0, infinity). Further more, we also present a detail analysis on the influence of m(x) on the limit behavior of minimizers as M -> infinity.

• 单位
  华中农业大学