An overview of unconstrained free boundary problems

An overview of unconstrained free boundary problems.

In this paper, we present a survey concerning unconstrained free boundary problems of type [Formula: see text] where B1 is the unit ball, Ω is an unknown open set, F(1) and F(2) are elliptic operators (admitting regular solutions), and [Formula: see text] is a functions space to be specified in each case. Our main objective is to discuss a unifying approach to the optimal regularity of solution...

An Efficient Conjugate Gradient Algorithm for Unconstrained Optimization Problems

In this paper, an efficient conjugate gradient method for unconstrained optimization is introduced. Parameters of the method are obtained by solving an optimization problem, and using a variant of the modified secant condition. The new conjugate gradient parameter benefits from function information as well as gradient information in each iteration. The proposed method has global convergence und...

Obstacle Problems and Free Boundaries: an Overview

Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries uses methods from PDEs, Calculus of Variations, Geometric Measure Theory, and Harmonic Analysis. The most important mathematical challenge in this context is ...

An Existence Result for a Class of Free Boundary Problems an Existence Result for a Class of Free Boundary Problems

In this paper we study the existence of C 2;; domain solutions for a class of free boundary problems which are critical domains for a shape functional depending on a general term (in most PDE applications this term represents the energy associated) and the perimeter, under the constraint that the measure of is given. As an application there are considered two problems. They involve respectively...

On Free Boundary Problems