论文标题
弱解决方案的Hölder连续性对生物运输网络建模
Hölder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network
论文作者
论文摘要
在本文中，我们研究了椭圆形 - 羟基蛋白网络系统自然网络形成的弱解决方案的规律性。该系统是奇异的，涉及立方非线性。我们的调查表明，当太空尺寸$ n $ $ 2 $时，弱解决方案是连续的。这是通过与斯塔默尔 - 喀托的功能类别相关的不平等以及最初是由于S. campanato和C. B. Morrey（\ cite {g}，第86页）的诱饵的细化而实现的。
In this paper we study the regularity of weak solutions to an elliptic-parabolic system modeling natural network formation. The system is singular and involves cubic nonlinearity. Our investigation reveals that weak solutions are Hölder continuous when the space dimension $N$ is $2$. This is achieved via an inequality associated with the Stummel-Kato class of functions and refinement of a lemma originally due to S. Campanato and C. B. Morrey (\cite{G}, p. 86).
