Harnack type inequality and a priori estimates for solutions of a class of semilinear elliptic equations

3Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

For dimensions 3 ≤ n ≤ 6, we derive here the Harnack type inequalityunder(max, BR) u ṡ under(min, B2 R) u ≤ frac(C, Rn - 2) for C2, positive solutions u ofΔ u - μ u + K (x) ufrac(n + 2, n - 2) = 0 in ball B (0, 3 R) in Rn where R ≤ 1. Here μ > 0 and the constant C = C (n, μ, | K |, | ∇ K |). For dimension 3, we assume that K is Hölder continuous with exponent θ with frac(1, 2) < θ ≤ 1. While for dimensions n = 4, 5, 6, assume that K ∈ C1 is bounded between two positive constants and that in a neighborhood of a critical point x0 of K, we havec | x - x0 |θ - 1 ≤ | ∇ K (x) | ≤ C | x - x0 |θ - 1 for c, C > 0 and frac(n - 2, 2) ≤ θ ≤ n - 2. As an application, a priori estimates for solutions are obtained in star shaped domains. © 2007 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Lin, C. S., & Prajapat, J. V. (2008). Harnack type inequality and a priori estimates for solutions of a class of semilinear elliptic equations. Journal of Differential Equations, 244(3), 649–695. https://doi.org/10.1016/j.jde.2007.09.012

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free