Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate i...Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate is proved for S-matrix. The so-called finite step convergence for coincident components is discussed for nondegenerate discreted problems.展开更多
A two-side obstacle problem in R^n is an important type of variationalinequalities, which can be generated by discrete mathematical and physical problemsor some other practical models directly. Consider a two-side obs...A two-side obstacle problem in R^n is an important type of variationalinequalities, which can be generated by discrete mathematical and physical problemsor some other practical models directly. Consider a two-side obstacle problem. Let f=Ax-q, . We want to find a vector x in K such展开更多
This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.
We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some c...We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some coercivity and growth conditions with the naturalexponent 1 〈 p 〈 n, the obstacle function φ≥ 0, and the boundary data θ ∈ W1mp（Ω）.展开更多
In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality.Existence,uniqueness and regularity of the optimal control,problem are establi...In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality.Existence,uniqueness and regularity of the optimal control,problem are established.In addition,the approximation of the optimal obstacle problem is also studied.展开更多
The Hǒlder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case 1<p<2
In this paper,we improved the regularity results of obstacle problems,in which the smooth conditions of the coefficients aij(x) are released from C1() to L∞(Ω).
This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the prob...This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.展开更多
In this paper, by investigating an optimal control problem which is equivalent to original problem, the regularity of an obstacle optimal control problem was treated. Furthermore, based on some properties of operator ...In this paper, by investigating an optimal control problem which is equivalent to original problem, the regularity of an obstacle optimal control problem was treated. Furthermore, based on some properties of operator T for the variational inequality problem, the existence and uniqueness of the original problem were proved.展开更多
In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator wh...In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator which has optimal approximation properties and preserves positivity. With the help of the interpolation operator the upper and lower bounds were obtained.展开更多
In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the ...In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the free boundaries.展开更多
In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily c...In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily convert to an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. The numerical examples and computational results illustrate and guarantee a higher accuracy for this technique.展开更多
This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically if a relation-shi...This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically if a relation-ship between the penalty parameter and the discretization parameter h is satisfied. An error estimate between the penalty solution and the discret penalty solution is provided. To validate the theoretical results, some numerical tests on one dimensional obstacle problem are presented.展开更多
Abstract In this paper the implicit obstacle problem of fully nonlinear second order elliptic equations associated with impulsive control problem are investigated.The comparion principle for viscosity solutions is pro...Abstract In this paper the implicit obstacle problem of fully nonlinear second order elliptic equations associated with impulsive control problem are investigated.The comparion principle for viscosity solutions is proved,the existence and uniqueness results are disscussed.展开更多
We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operat...We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.展开更多
This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12].
For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ...For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.展开更多
文摘Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate is proved for S-matrix. The so-called finite step convergence for coincident components is discussed for nondegenerate discreted problems.
文摘A two-side obstacle problem in R^n is an important type of variationalinequalities, which can be generated by discrete mathematical and physical problemsor some other practical models directly. Consider a two-side obstacle problem. Let f=Ax-q, . We want to find a vector x in K such
文摘This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.
基金supported by NSF of Hebei Province (07M003)supported by NSFC (10771195)NSF of Zhejiang Province(Y607128)
文摘We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some coercivity and growth conditions with the naturalexponent 1 〈 p 〈 n, the obstacle function φ≥ 0, and the boundary data θ ∈ W1mp（Ω）.
基金the National Natural Science Foundation of China(No.10472061)the Ph.D.Programs Foundation of Ministry of Education of China(No.20060280015)
文摘In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality.Existence,uniqueness and regularity of the optimal control,problem are established.In addition,the approximation of the optimal obstacle problem is also studied.
基金in part by Zhongshan University Science Research Fund
文摘The Hǒlder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case 1<p<2
基金This work was supported bythe National Natural Science Foundation of China(No.50306019,40375010,10471109,10471110 andA0324650).
文摘In this paper,we improved the regularity results of obstacle problems,in which the smooth conditions of the coefficients aij(x) are released from C1() to L∞(Ω).
基金Supported by the Key Grant Project of Chinese Ministry of Education (NO.309018)National Natural Science Foundation of China (NO.70973104,NO.11171304)Zhejiang Provincial Natural Science Foundation of China (NO.Y6110023)
文摘This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.
文摘In this paper, by investigating an optimal control problem which is equivalent to original problem, the regularity of an obstacle optimal control problem was treated. Furthermore, based on some properties of operator T for the variational inequality problem, the existence and uniqueness of the original problem were proved.
基金Project supported by National Natural Science Foundation ofChina (Grant No .10471089)
文摘In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator which has optimal approximation properties and preserves positivity. With the help of the interpolation operator the upper and lower bounds were obtained.
基金supported by the National Key R&Dprogram of China(2021YFA1003001)。
文摘In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the free boundaries.
文摘In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily convert to an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. The numerical examples and computational results illustrate and guarantee a higher accuracy for this technique.
文摘This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically if a relation-ship between the penalty parameter and the discretization parameter h is satisfied. An error estimate between the penalty solution and the discret penalty solution is provided. To validate the theoretical results, some numerical tests on one dimensional obstacle problem are presented.
文摘Abstract In this paper the implicit obstacle problem of fully nonlinear second order elliptic equations associated with impulsive control problem are investigated.The comparion principle for viscosity solutions is proved,the existence and uniqueness results are disscussed.
文摘We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.
基金The project was supported by the National Natural Science Foundation of China
文摘This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12].
基金supported by National Natural Science Foundation of China (Grant No. 10971224)Natural Science Foundation of Hebei Province (Grant No. A2011201011)
文摘For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.
