Minimization of eigenvalues for a quasilinear elliptic Neumann problem with indefinite weight

作者：Derlet A; Gossez J P^*; Takac P

来源：Journal of Mathematical Analysis and Applications, 2010, 371(1): 69-79.

DOI：10.1016/j.jmaa.2010.03.068

• p-Laplacian
• Neumann problem
• Indefinite weight
• Principal eigenvalue
• Optimization

We investigate the minimization of the positive principal eigenvalue of the problem -Delta(p)u = lambda m vertical bar u vertical bar(p-2)u in Omega, partial derivative u/partial derivative nu = 0 on partial derivative Omega, over a class of sign-changing weights m with integral(Omega) m < 0. It is proved that minimizers exist and satisfy a bang-bang type property. In dimension one, we obtain a complete description of the minimizers. This problem is motivated by applications from population dynamics.

• 出版日期2010-11-1