Doubling properties for second order parabolic equations - In memory of Eugene!Fabes

• 成果类型: Article
• 署名作者: Safonov, MV; Yuan, Y
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121104
• 发表日期: 1999
• 页码: 313-327
• 关键词: nonnegative solutions; harnack inequality; boundary-behavior; domains; form

摘要

We prove the doubling property of L-caloric measure corresponding to the second order parabolic equation in the whole space and in Lipschitz domains. For parabolic equations in the divergence form, a weaker form of the doubling property follows easily from a recent result, the backward Harnack inequality, and known estimates of Green's function. Our method works for both the divergence and nondivergence cases. Moreover, the backward Harnack inequality and estimates of Green's function are not needed in the course of proof.