In this work, we present a novel power penalty method for the approximation of a global solution to a double obstacle complementarity problem involving a semilinear parabolic differential operator and a bounded feasible solution set. We first rewrite the double obstacle complementarity problem...

This paper is intended to give a representation for a stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized backward doubly stochastic differential equations.

First, let u <Subscript> g </Subscript> be the unique solution of an elliptic variational inequality with source term g. We establish, in the general case, the error estimate between <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$u_{3}(\mu)=\mu u_{g_{1}}+ (1-\mu)u_{g_{2}}$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$u_{4}(\mu)=u_{\mu g_{1}+ (1-\mu) g_{2}}$</EquationSource> </InlineEquation> for μ∈[0,1]. Secondly, we consider a...</equationsource></inlineequation></equationsource></inlineequation></subscript>

Electrical impedance tomography (EIT) is a relatively new imaging modality in which the internal resistivity distribution is reconstructed based on the known sets of injected currents and measured voltages on the surface of the object.