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Continuity results for degenerate diffusion equations with LtpLxq drifts
Nonlinear Analysis ( IF 1.3 ) Pub Date : 2021-05-28 , DOI: 10.1016/j.na.2021.112413 Sukjung Hwang , Yuming Paul Zhang
中文翻译:
退化扩散方程的连续性结果 漂移
更新日期:2021-05-28
Nonlinear Analysis ( IF 1.3 ) Pub Date : 2021-05-28 , DOI: 10.1016/j.na.2021.112413 Sukjung Hwang , Yuming Paul Zhang
In this paper, we study local uniform continuity of nonnegative weak solutions to degenerate diffusion-drift equations in the form of assuming a vector field . Regarding local Hölder continuity, we provide a sharp condition on and , which is referred to as the subcritical region. In the critical region, the divergence-free condition is essential to providing uniform continuity which depends on the modulus of continuity of the local norm of .
中文翻译:
退化扩散方程的连续性结果 漂移
在本文中,我们研究了退化扩散漂移方程的非负弱解的局部均匀连续性,其形式为 假设向量场 . 关于局部 Hölder 连续性,我们提供了一个尖锐的条件 和 ,称为亚临界区。在临界区,无散度条件对于提供均匀连续性至关重要,这取决于局部范数的连续性模数.