Blow-up rates of large solutions for elliptic equations☆

By Zhijun Zhang, Yun-Jie Ma, Ling Mi, Xiaohong Li. 2010

55 citations recorded by the source corpus.

In this paper, we mainly study the boundary behavior of solutions to boundary blow-up elliptic problems for more general nonlinearities f (which may be rapidly varying at infinity) Δu=b(x)f(u), x∈Ω, u|∂Ω=+∞, where Ω is a bounded domain with smooth boundary in RN, and b∈Cα(Ω¯) which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary. Further, when f(s)=sp±f1(s) for s sufficiently large, where p>1 and f1 is normalized regularly varying at infinity with index p1∈(0,p), we show the influence of the geometry of Ω on the boundary behavior for solutions to the problem. We also give the existence and uniqueness of solutions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/506f53411bab332167a7e527d68582139e4891c4

Citations in the corpus

• Boundary behavior of large solutions to the Monge-Ampère equations with weights (2015, unknown): “3), see, for instance, [1,2,10,11,14–16,27,43,47] and the references therein.”