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

• Datum: 2008
• Hauptverfasser: Antoniouk, A. Val., Antoniouk, A. Vict., Антонюк, О. Вал., Антонюк, О. Вік.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2008
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3245
• Назва журналу: 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...