OBSTACLE PROBLEMS ON RCD(K,N)METRIC MEASURE SPACES

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.

Monotone Additive Schwarz Algorithms for Solving Two-Side Obstacle Problems

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.

Residual-type a posteriori error estimate for parabolic obstacle problems

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.

Regularity of solutions of obstacle problems

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).

LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS

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.

LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

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）.

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

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

ERROR REDUCTION IN ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC OBSTACLE PROBLEMS

We consider an adaptive finite element method （AFEM） for obstacle problems associated with linear second order elliptic boundary value problems and prove a reduction in the energy norm of the discretization error which leads to R-linear convergence. This result is shown to hold up to a consistency error due to the extension of the discrete multipliers （point functionals） to H^-1 and a possible mismatch between the continuous and discrete coincidence and noncoincidence sets. The AFEM is based on a residual-type error estimator consisting of element and edge residuals. The a posteriori error analysis reveals that the significant difference to the unconstrained case lies in the fact that these residuals only have to be taken into account within the discrete noncoincidence set. The proof of the error reduction property uses the reliability and the discrete local efficiency of the estimator as well as a perturbed Galerkin orthogonality. Numerical results are given illustrating the performance of the AFEM.

Global Integrability for Solutions to Obstacle Problems

DenoteκψØ(Ω)={υ∈w1,p(Ω):υ≥ψ,a,e.andυ-Ø∈w1,po(Ω)},where is any function in Q C R^(N),N≥2,with values in RU[±∞]and e is a measurable function.This paper deals with global integrability for u E Kμ,e such that∫Ω﹤Α(χ,▽υ),▽(w-u)﹥dx≥∫Ω﹤f,▽(w-u)dx,■w∈■ψØ(Ω),with/A■≈|■|^(p-1),1<p<N.Some global integrability results are obtained.

DIRICHLET PROBLEM FOR THE IMPLICIT OBSTACLE PROBLEMS

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.

Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems Via a Sequence of Penalized Equations

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.

Optimal investment with transaction costs based on exponential utility function:a parabolic double obstacle problem

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.

Optimal obstacle control problem

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.

Regularity of obstacle optimal control problem

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.

A PRIORI ERROR ESTIMATES FOR OBSTACLE OPTIMAL CONTROL PROBLEM,WHERE THE OBSTACLE IS THE CONTROLITSELF

In this paper we deal with the convergence analysis of the finite element method for an elliptic penalized unilateral obstacle optimal control problem where the control and the obstacle coincide.Error estimates are established for both state and control variables.We apply a fixed point type iteration method to solve the discretized problem.To corroborate our error estimations and the eficiency of our algorithms,the convergence results and numerical experiments are illustrated by concrete examples.

ON THE ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT APPROXIMATION TO THE OBSTACLE PROBLEM

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].

The Keldys-Fichera Obstacle Problem

In this paper we consider a quasilinear obstacle problem with coefficients of higher growth orders and the Keldys-Fichera boundary condition.

ENTROPY SOLUTIONS FOR FIRST-ORDER QUASILINEAR EQUATIONS RELATED TO A BILATERAL OBSTACLE CONDITION IN A BOUNDED DOMAIN

This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of Rp, p>= 1. The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform L -estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L . The uniqueness of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in Lq of approximate solutions to U.

THE C^(1,α) REGULARITY OF SOLUTIONS TO DOUBLE OBSTACLE PROBLEM OF VARIATIONAL INEQUALITY

In this paper, a double obstacle problem of variational inequalities is considered and its solutions is obtained. The results of one-sided obstacle problem are not required in the analysis of our main results, which is different from the previous works.

Mathematical Justification of an Obstacle Problem in the Case of a Plate

In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified. Starting from the three-dimensional nonlinear Signorini problem, by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied. It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.