We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k...We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.展开更多
In this paper,we study the problem of analyticity of smooth solutions of the inviscid Boussinesq equations.If the initial datum is real-analytic,the solution remains real-analytic on the existence interval.By an induc...In this paper,we study the problem of analyticity of smooth solutions of the inviscid Boussinesq equations.If the initial datum is real-analytic,the solution remains real-analytic on the existence interval.By an inductive method we can obtain a lower bound on the radius of spatial analyticity of the smooth solution.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11171339 and 11171261)National Center for Mathematics and Interdisciplinary Sciences
文摘We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.
基金supported partially by"The Fundamental Research Funds for Central Universities of China".
文摘In this paper,we study the problem of analyticity of smooth solutions of the inviscid Boussinesq equations.If the initial datum is real-analytic,the solution remains real-analytic on the existence interval.By an inductive method we can obtain a lower bound on the radius of spatial analyticity of the smooth solution.
