Abstract
We study a Dirichlet optimal control problem for a nonlinear elliptic anisotropic p-Laplace equation with control and state constraints. The matrix-valued coecients we take as controls and in the linear part of dierential operator we consider coecients to be unbounded skew-symmetric matrix. We show that, in spite of unboundedness of the non-linear dierential operator, the considered Dirichlet problem admits at least one weak solution and the corresponding OCP is well-possed and solvable.
Highlights
In this paper we deal with the following optimal control problem (OCP) for nonlinear elliptic equation with unbounded coefficientsMinimize I(A, y) = y − yd p Lp(Ω) + εΩ |As21ym∇y|pRN dx subject to the constraints (1.1) p−2−div |(Asym∇y, ∇y)| 2 Asym∇y − div Askew∇y = −div f, Asym ∈ Aad, y ∈ W01,p(Ω) (1.2) (1.3)where p satisfies 2 < p < +∞, ε > 0 is a small fixed parameter, the symmetric matrix of anisotropy Asym ∈ L∞(Ω; RN×N ) ∩ BV (Ω; RN×N ) is taken as a control, the skew-symmetric matrix Askew ∈ Lq(Ω; RN×N ) is a given matrix of coefficients, yd ∈ Lp(Ω) and f ∈ Lq(Ω; RN ) are given distributions
We study a Dirichlet optimal control problem for a nonlinear elliptic anisotropic pLaplace equation with control and state constraints
In spite of unboundedness of the non-linear differential operator, the considered Dirichlet problem admits at least one weak solution and the corresponding OCP is well-possed and solvable
Summary
We study a Dirichlet optimal control problem for a nonlinear elliptic anisotropic pLaplace equation with control and state constraints. The matrix-valued coefficients Asym ∈ L∞(Ω; SNsym) we take as controls and in the linear part of differential operator we consider coefficients to be unbounded skew-symmetric matrix Askew ∈ Lq(Ω; SNskew). In spite of unboundedness of the non-linear differential operator, the considered Dirichlet problem admits at least one weak solution and the corresponding OCP is well-possed and solvable
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
