Nonexistence of multi-bubble solutions to some elliptic equations on convex domains

作者：Grossi Massimo^*; Takahashi Futoshi

来源：Journal of Functional Analysis, 2010, 259(4): 904-917.

DOI：10.1016/j.jfa.2010.03.008

• Blowing-up solution
• Liouville equation
• Critical Sobolev exponent

We prove the nonexistence of multi-bubble solutions for several types of problems on smooth-bounded convex domains. Problems we study include the Liouville equation
-Delta u = lambda e(u) in Omega, u = 0 on partial derivative Omega
in R(2), where lambda > 0 is a parameter, and the almost critical problem
-Delta u = u(N+2/N-2 - epsilon), u > 0 in Omega, u = 0 on partial derivative Omega
in higher dimensions, where epsilon > 0.

• 出版日期2010-8-15