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A priori estimates, existence and non-existence of positive solutions of generalized mean curvature equations

✍ Scribed by Qiuyi Dai; Yonggeng Gu; Jiuyi Zhu

Book ID: 113811391
Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 246 KB
Volume: 74
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2011.07.034

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## Abstract We study the initial value problem where $ \|u(\cdot,t)\| = \int \nolimits ^ {\infty} \_ {- \infty}\varphi(x) | u( x,t ) | {\rm{ d }} x$ with φ(__x__)⩾0 and $ \int \nolimits^{\infty} \_ {-\infty} \varphi (x) \, {\rm{d}}x\,= 1$. We show that solutions exist globally for 0<__p__⩽1, while