ﻻ يوجد ملخص باللغة العربية
We consider shape optimization problems for general integral functionals of the calculus of variations, defined on a domain $Omega$ that varies over all subdomains of a given bounded domain $D$ of ${bf R}^d$. We show in a rather elementary way the existence of a solution that is in general a quasi open set. Under very mild conditions we show that the optimal domain is actually open and with finite perimeter. Some counterexamples show that in general this does not occur.
The paper studies a class of variational problems, modeling optimal shapes for tree roots. Given a measure $mu$ describing the distribution of root hair cells, we seek to maximize a harvest functional $mathcal{H}$, computing the total amount of water
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin condition on
The $Gamma $-limit of a family of functionals $umapsto int_{Omega }fleft( frac{x}{varepsilon },frac{x}{varepsilon ^{2}},D^{s}uright) dx$ is obtained for $s=1,2$ and when the integrand $f=fleft( y,z,vright) $ is a continous function, periodic in $y$ a
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems, based on
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the opti