On a singular semilinear elliptic boundary value problem and the boundary Harnack principle

Athreya, Siva (2002) On a singular semilinear elliptic boundary value problem and the boundary Harnack principle Potential Analysis, 17 (3). pp. 293-301. ISSN 0926-2601

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Official URL: http://link.springer.com/article/10.1023/A:1016122...

Related URL: http://dx.doi.org/10.1023/A:1016122901605

Abstract

On a bounded C2-domain D⊂Rd we consider the singular boundary-value problem 1/2Δu=f(u) in D, u∂D=φ, where d≥3, f:(0,∞)→(0,∞) is a locally Holder continuous function such that f(u)→∞ as u→0 at the rate u−α, for some α∈(0,1), and φ is a non-negative continuous function satisfying certain growth assumptions. We show existence of solutions bounded below by a positive harmonic function, which are smooth in D and continuous in ̅D. Such solutions are shown to satisfy a boundary Harnack principle.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:Semi-linear Partial Differential Equations; Boundary Harnack Principle
ID Code:100519
Deposited On:12 Feb 2018 12:17
Last Modified:12 Feb 2018 12:17

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