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

• Published in: Український математичний журнал
• Date: 2008
• Main Authors: Antoniouk, A.Val., Antoniouk, A.Vict.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164759
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Continuity with respect to initial data and absolute-continuity approach to the first-order regularity of nonlinear diffusions on noncompact manifolds / A.Val. Antoniouk, A.Vict. Antoniouk // Український математичний журнал. — 2008. — Т. 60, № 10. — С. 1299–1316. — Бібліогр.: 14 назв. — англ.

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