Density theorems for local minimizers of area-type functionals
Design-dependent loads in topology optimization
We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset of a reference domain, and the complement of is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure , which is the total work of the pressure and...
Design-dependent loads in topology optimization
We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S, which is the total work of the pressure...
DiPerna-Majda measures and uniform integrability
The purpose of this note is to discuss the relationship among Rosenthal's modulus of uniform integrability, Young measures and DiPerna-Majda measures. In particular, we give an explicit characterization of this modulus and state a criterion of the uniform integrability in terms of these measures. Further, we show applications to Fatou's lemma.
Discontinuous solutions in problems of optimization
Discrete approximation of the Mumford-Shah functional in dimension two
Discrete approximation of the Mumford-Shah functional in dimension two
The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of vergence by a sequence of integral functionals defined on piecewise affine functions.
Discrete thickness
We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the discrete energies...
Diseguaglianze isoperimetriche e diseguaglianze di Sobolev
Distance between components in optimal design problems with perimeter penalization
Disuguaglianze di Sobolev nello spazio iperbolico bidimensionale
Double bubbles in the three-torus.