Indefinite elliptic problems in a domain
Abstract
In this paper, we study the elliptic boundary value problem in a bounded domain Ω in Rn, with smooth boundary: { -Δu = R(x)cp u > 0 x ∈ Ω { u(x) = 0 x ∈ ∂Ω. where R(x) is a smooth function that may change signs. In [2], using a blowing up argument, Berestycki, Dolcetta, and Nirenberg, obtained a priori estimates and hence the existence of solutions for the problem when the exponent 1 < p < n+2/n-1. Inspired by their result, in this article, we use the method of moving planes to fill the gap between n+2/n-1 and the critical Sobolev exponent n+2/n-1. We obtain a priori estimates for the solutions for all 1 < p < n+2/n-1.
Department(s)
Mathematics
Document Type
Article
DOI
https://doi.org/10.3934/dcds.1997.3.333
Keywords
A priori estimates, Indefinite nonlinear elliptic equations, Method of moving planes
Publication Date
1-1-1997
Recommended Citation
Chen, Wenxiong, and Congming Li. "Indefinite elliptic problems in a domain." Discrete & Continuous Dynamical Systems 3, no. 3 (1997): 333.
Journal Title
Discrete and Continuous Dynamical Systems
