In this paper, the Cauchy problem of the degenerate parabolic equationsis studied for some cases, and the explicit Holder estimates of the solution u with respectto x is given.
In this paper we are concerned with the global regularity of solutions to the Dirichlet problem for a class of Monge-Ampère type equations.By employing the concept of(a,η) type domain,we emphasize that the bound...In this paper we are concerned with the global regularity of solutions to the Dirichlet problem for a class of Monge-Ampère type equations.By employing the concept of(a,η) type domain,we emphasize that the boundary regularity depends on the convexity of the domain in nature.The key idea of our proof is to provide more effective global H?lder estimates of convex solutions to the problem based on carefully choosing auxiliary functions and constructing sub-solutions.展开更多
文摘In this paper, the Cauchy problem of the degenerate parabolic equationsis studied for some cases, and the explicit Holder estimates of the solution u with respectto x is given.
基金Yau Mathematical Sciences Center for the support。
文摘In this paper we are concerned with the global regularity of solutions to the Dirichlet problem for a class of Monge-Ampère type equations.By employing the concept of(a,η) type domain,we emphasize that the boundary regularity depends on the convexity of the domain in nature.The key idea of our proof is to provide more effective global H?lder estimates of convex solutions to the problem based on carefully choosing auxiliary functions and constructing sub-solutions.
