Some Remarks on Infinite-dimensional Nonlinear Elliptic Problems

A numerical method for solving nonlinear partial differential equations based on Sinc-Galerkin method

In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla u)) = f $. Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.

Regularity for obstacle problems in infinite dimensional Hilbert spaces

In this paper we study fully nonlinear obstacle type problems in Hilbert spaces. We introduce the notion of Q-elliptic equation and prove existence, uniqueness, and regularity of viscosity solutions of Q-elliptic obstacle problems. In particular we show that solutions of concave problems with semiconvex obstacles are in the space W 2,∞ Q .

A numerical verification method for solutions of nonlinear elliptic problems by an infinite dimensional Newton-type formulation

Stability of infinite dimensional control problems with pointwise state constraints

A general class of nonlinear infinite dimensional optimization problems is considered that covers semi-linear elliptic control problems with distributed control as well as boundary control. Moreover, pointwise inequality constraints on the control and the state are incorporated. The general optimization problem is perturbed by a certain class of perturbations, and we establish convergence of lo...

Asymptotic Boundary Conditions and Numerical Methods for Nonlinear Elliptic Problems

We present a derivation and implementation of asymptotic boundary conditions to be imposed on "artificial" boundaries for nonlinear elliptic boundary value problems on semi-infinite "cylindrical" domains. A general theory developed by the authors in [11] is applied to establish the existence of exact boundary conditions and then to obtain useful approximations to them. The derivation is based o...