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
The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poin...The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poincar'e inequalities.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
Let u = （Uh,U3） be a smooth solution of the 3-D Navier-Stokes equations in R3 × [0, T）. It was proved that if u3 ∈ L^∞（0,T;Bp,q-1＋3/p（R3）） for 3 〈 p,q 〈 oe and uh ∈ L^∞（0, T;BMO-1（R3）） with uh（...Let u = （Uh,U3） be a smooth solution of the 3-D Navier-Stokes equations in R3 × [0, T）. It was proved that if u3 ∈ L^∞（0,T;Bp,q-1＋3/p（R3）） for 3 〈 p,q 〈 oe and uh ∈ L^∞（0, T;BMO-1（R3）） with uh（T） ∈ VMO-1（R3）, then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al. （2016）, which requires u ∈ L^∞（O,T;Bp,^-11＋3/P（R3））. Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest.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.
基金supported by the National Natural Science Foundation of China(No.10971148)
文摘The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poincar'e inequalities.
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.
基金supported by National Natural Science Foundation of China (Grant Nos. 11301048, 11371039 and 11425103)the Fundamental Research Funds for the Central Universities
文摘Let u = （Uh,U3） be a smooth solution of the 3-D Navier-Stokes equations in R3 × [0, T）. It was proved that if u3 ∈ L^∞（0,T;Bp,q-1＋3/p（R3）） for 3 〈 p,q 〈 oe and uh ∈ L^∞（0, T;BMO-1（R3）） with uh（T） ∈ VMO-1（R3）, then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al. （2016）, which requires u ∈ L^∞（O,T;Bp,^-11＋3/P（R3））. Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest.
