孔令海; 郇中丹; 郭柏灵
Kong Linghai; Huan Zhongdan; Guo Boling
摘要:
In this article, the authors consider equation ut={\rm div}(\varphi (\Gamma u ) A(|D u|2)Du)-(u-I), where $\varphi $ is strictly positive and $\Gamma $ is a known vector-valued mapping, $A: {\Bbb R}_{+}\rightarrow {\Bbb R}^{+}$ is decreasing and $A(s)\sim 1/\sqrt{s} $ as $s\rightarrow +\infty $. This kind
of equation arises naturally from image denoising. For an initial datum $I \in {\rm BV}_{\rm loc}\cap L^{\infty},$ the existence of BV solutions to the initial value problem of the equation is obtained.
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