Continuity with respect to initial data and absolute-continuity approach to the first-order regularity of nonlinear diffusions on noncompact manifolds

• Date: 2008
• Main Authors: Antoniouk, A. Val., Antoniouk, A. Vict., Антонюк, О. Вал., Антонюк, О. Вік.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3245
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study the dependence on initial data for solutions of diffusion equations with globally non-Lipschitz coefficients on noncompact manifolds. Though the metric distance may not be everywhere twice differentiable, we show that, under certain monotonicity conditions on the coefficients and curvature...