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We consider the shape derivative formula for a volume cost functional studied in previous papers where we used the Minkowski deformation and support functions in the convex setting. In this work, we extend it to some non-convex domains, namely the star-shaped ones. The formula happens to be also an extension of a well-known one in the geometric Brunn-Minkowski theory of convex bodies. At the end, we illustrate the formula by applying it to some model shape optimization problem. [ABSTRACT FROM AUTHOR]

In this article, we deal with a numerical method for the approximation of a class of coupled shape optimization problems, which consist in minimizing an appropriate general volume cost functional subjected to coupled boundary value problems by means of a Neumann boundary transmission condition. We show the existence of the shape derivative of the cost functional and express it by means of support functions, using a new formula of shape derivative on a family of convex domains. This allows us to avoid the disadvantages related to the classical shape derivative method using vectors field. Then the numerical discretization is performed using the dual reciprocity boundary element method in order to avert the remeshing task required for the finite element method. Finally, we give some numerical results, based on the gradient method, showing the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this work, we consider the inverse problem of identifying a Robin coefficient in a nonlinear elliptic equation with mixed boundary conditions. We firstly reformulate the inverse problem as a regularized optimal control one, where the functional cost is of type L 1 - L 2 ; then we prove the existence and uniqueness of a minimizer to the resulting optimization problem in a suitable functional space. Finally, we provide a primal-dual algorithm to solve the variational problem and give some numerical results that prove the accuracy of the proposed method in the identification of the Robin coefficient. [ABSTRACT FROM AUTHOR]

The aim of this paper is to compute the shape derivative of a volume cost functional subject to a Dirich- let boundary value state constraint problem using the shape derivative formula introduced in (Boulkhemair et al., 2020), which concerns star-shaped domains. This allows us to express the shape derivative by means of support functions of convex domains. Then we give a simple algorithm for the numerical resolution of this problem. [ABSTRACT FROM AUTHOR]

The multiframe super-resolution (SR) techniques are considered as one of the active research fields. More precisely, the construction of the desired high resolution (HR) image with less artifacts in the SR models, which are always ill-posed problems, requires a great care. In this paper, we propose a new fourth-order equation based on a diffusive tensor that takes the benefit from the diffusion model of Perona-Malik in the flat regions and the Weickert model near boundaries with a high diffusion order. As a result, the proposed SR approach can efficiently preserve image features such as corner and texture much better with less blur near edges. The existence and uniqueness of the proposed partial differential equation (PDE) are also demonstrated in an appropriate functional space. Finally, the given experimental results show the effectiveness of the proposed PDE compared to some competitive methods in both visually and quantitatively. [ABSTRACT FROM AUTHOR]