Optimal L1-Control in Coefficients for Dirichlet Elliptic Problems: W-Optimal Solutions

Weak Optimal Controls in Coefficients for Linear Elliptic Problems

In this paper we study an optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. The equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions. We adopt the weight function as a control in L1(Ω). Using the direct method in the Calculus of variations, we discuss the solvability of this optimal control p...

Aleksandra Orpel CONTINUOUS DEPENDENCE OF SOLUTIONS OF ELLIPTIC BVPs ON PARAMETERS

The continuous dependence of solutions for a certain class of elliptic PDE on functional parameters is studied in this paper. The main result is as follow: the sequence {xk}k∈N of solutions of the Dirichlet problem discussed here (corresponding to parameters {uk}k∈N ) converges weakly to x0 (corresponding to u0) in W 1,q 0 (Ω, R), provided that {uk}k∈N tends to u0 a.e. in Ω. Our investigation c...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Elliptic Equations with Bmo Coefficients in Lipschitz Domains

In this paper, we study inhomogeneous Dirichlet problems for elliptic equations in divergence form. Optimal regularity requirements on the coefficients and domains for the W 1,p (1 < p < ∞) estimates are obtained. The principal coefficients are supposed to be in the John-Nirenberg space with small BMO semi-norms. The domain is supposed to have Lipschitz boundary with small Lipschitz constant. T...

On unbounded optimal controls in coefficients for ill-posed elliptic Dirichlet boundary value problems

We consider an optimal control problem associated to Dirichlet boundary value problem for linear elliptic equations on a bounded domain Ω. We take the matrixvalued coe cients A(x) of such system as a control in L(Ω;R × R ). One of the important features of the admissible controls is the fact that the coe cient matrices A(x) are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric par...