We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local mini...We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.展开更多
For the initial boundary value problem about a type of parabolicMonge Ampe re equation of the form (IBVP):{-D tu+( det D^(2)_(x)u) 1/n =f(x,t),(x,t)∈Q= Ω ×(0,T],u(x,t)=(x,t)(x,t)∈ pQ},where Ω is a ...For the initial boundary value problem about a type of parabolicMonge Ampe re equation of the form (IBVP):{-D tu+( det D^(2)_(x)u) 1/n =f(x,t),(x,t)∈Q= Ω ×(0,T],u(x,t)=(x,t)(x,t)∈ pQ},where Ω is a bounded convex domain in R n ,the result in by Ivochkina and Ladyzheskaya is improved in the sense that, under assumptions that the data of the problem possess lower regularity and satisfy lower order compatibility conditions than those in , the existence of classical solution to (IBVP) is still established (see Theorem 1.1 below). This can not be realized by only using the method in . The main additional effort the authors have done is a kind of nonlinear perturbation.展开更多
文摘We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.
文摘For the initial boundary value problem about a type of parabolicMonge Ampe re equation of the form (IBVP):{-D tu+( det D^(2)_(x)u) 1/n =f(x,t),(x,t)∈Q= Ω ×(0,T],u(x,t)=(x,t)(x,t)∈ pQ},where Ω is a bounded convex domain in R n ,the result in by Ivochkina and Ladyzheskaya is improved in the sense that, under assumptions that the data of the problem possess lower regularity and satisfy lower order compatibility conditions than those in , the existence of classical solution to (IBVP) is still established (see Theorem 1.1 below). This can not be realized by only using the method in . The main additional effort the authors have done is a kind of nonlinear perturbation.
