Antimaximum principle in exterior domains

作者：Anoop T V; Drabek P^*; Sankar Lakshmi; Sasi Sarath

来源：Nonlinear Analysis-Theory Methods & Applications, 2016, 130: 241-254.

DOI：10.1016/j.na.2015.10.010

• Exterior domains
• p-Laplacian
• Local and global antimaximum
• principle Positive eigenfunctions
• Regularity results

We consider the antimaximum principle for the p-Laplacian in the exterior domain:
{-Delta pu = lambda K (x) vertical bar mu vertical bar(p-2)u+h(x) in B-1(c)
u=0 on partial derivative B-1,
where Delta(p) is the p-Laplace operator with p > 1, A is the spectral parameter and B-1(c) is the exterior of the closed unit ball in RN with N >= 1. The function h is assumed to be nonnegative and nonzero, however the weight function K is allowed to change its sign. For K in a certain weighted Lebesgue space, we prove that the antimaximum principle holds locally. A global antimaximum principle is obtained for h with compact support. For a compactly supported K, with N = 1 and p = 2, we provide a necessary and sufficient condition on h for the global antimaximum principle. In the course of proving our results we also establish the boundary regularity of solutions of certain boundary value problems.

• 出版日期2016-1