| Autor: |
Bögelein, Verena, Stanin, Thomas |
| Zdroj: |
Annali di Matematica Pura ed Applicata; Apr2020, Vol. 199 Issue 2, p573-587, 15p |
| Abstrakt: |
We establish a local Lipschitz regularity result of solutions to the Cauchy–Dirichlet problem associated with evolutionary partial differential equations ∂ t u - div D f (∇ u) = 0 , in Ω T , u = u 0 , on ∂ P Ω T. We do not impose any growth assumptions from above on the function f : R n → R and only require it to be convex and coercive. The domain Ω is required to be bounded and convex, and the time-independent boundary datum u 0 is supposed to be convex and Lipschitz continuous on Ω ¯ . It can be seen as an evolutionary analogue to the one-sided bounded slope condition. Additionally, assuming Ω to be uniformly convex, we establish global continuity on Ω T ¯ of the solution. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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