The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. T...The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.展开更多
We consider algebras with basis numerated by elements of a group G. We fix a function f from G × G to a ground field and give a multiplication of the algebra which depends on f. We study the basic properties of s...We consider algebras with basis numerated by elements of a group G. We fix a function f from G × G to a ground field and give a multiplication of the algebra which depends on f. We study the basic properties of such algebras. In particular, we find a condition on f under which the corresponding algebra is a Leibniz algebra. Moreover, for a given subgroup G of G we define a G-periodic algebra, which corresponds to a G-periodic function f, we establish a criterion for the right nilpotency of a G-periodic algebra. In addition, for （7 = Z we describe all 2Z- and 3Z-periodic algebras. Some properties of nZ-periodic algebras are obtained.展开更多
In this paper we estimate the solutions of homogeneous linear system of differential equations with unbounded coefficients on the real line R. We also give a necessary and sufficient condition in order that the linear...In this paper we estimate the solutions of homogeneous linear system of differential equations with unbounded coefficients on the real line R. We also give a necessary and sufficient condition in order that the linear differential operator with unbounded coefficients has a bounded inverse in the scalar case.展开更多
基金The project supported by the China-Germany Cooperation Project under Grant No. 446 CHV 113/231, ＂Quantum information and related mathematical problems＂ and National Natural Science Foundation of China under Grant Nos. 10375038 and 10271081
文摘The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.
文摘We consider algebras with basis numerated by elements of a group G. We fix a function f from G × G to a ground field and give a multiplication of the algebra which depends on f. We study the basic properties of such algebras. In particular, we find a condition on f under which the corresponding algebra is a Leibniz algebra. Moreover, for a given subgroup G of G we define a G-periodic algebra, which corresponds to a G-periodic function f, we establish a criterion for the right nilpotency of a G-periodic algebra. In addition, for （7 = Z we describe all 2Z- and 3Z-periodic algebras. Some properties of nZ-periodic algebras are obtained.
文摘In this paper we estimate the solutions of homogeneous linear system of differential equations with unbounded coefficients on the real line R. We also give a necessary and sufficient condition in order that the linear differential operator with unbounded coefficients has a bounded inverse in the scalar case.
