Free boundary regularity for a multiphase shape optimization problem
نویسندگان
چکیده
منابع مشابه
Analytic regularity of a free boundary problem
In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most n− 8. Mathematics Subject Classification (2000): 49Q20
متن کاملA Bilevel Shape Optimization Problem for the Exterior Bernoulli Free Boundary Value Problem
A bilevel shape optimization problem with the exterior Bernoulli free boundary problem as lower-level problem and the control of the free boundary as the upper-level problem is considered. Using the shape of the inner boundary as the control, we aim at reaching a specific shape for the free boundary. A rigorous sensitivity analysis of the bilevel shape optimization in the infinite-dimensional s...
متن کاملShape optimization for free boundary problems
In this paper three different formulations of a Bernoulli type free boundary problem are discussed. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is ...
متن کاملMultiphase Shape Optimization Problems
This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as min { g ( (F1(Ω1), . . . , Fh(Ωh) ) +m ∣∣ h ⋃ i=1 Ωi ∣∣ : Ωi ⊂ D, Ωi ∩ Ωj = ∅}, where D ⊆ R is a given bounded open set, |Ωi| is the Lebesgue measure of Ωi and m is a positive constant. For a large class of such functionals, we analyse qualitative properties of the cells and the int...
متن کاملShape Optimization and Trial Methods for Free Boundary Problems Shape Optimization and Trial Methods for Free Boundary Problems
In this work we consider diierent formulations for a free boundary problem and analyze the related numerical methods. In particular, we formulate various shape optimization problems that are weak forms of a free boundary problem and analyze their properties using the tools of 'shape calculus'. The main result is that it is possible to innuence the conditioning of the shape cost functional and t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2019
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2019.1658773