A new compact class of open sets under Hausdorff distance and shape optimization

2010/03/20 by Donghui Yang, Yang, Donghui
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Optimization and Control (math.OC) #math.GN #math.OC

paper · pdf · doi:10.48550/arxiv.1004.2874

arxiv created 2010/08/16 · arxiv updated 2010/08/17

Abstract

In this paper we obtain a new class of open sets, and we prove the class is compact under the Hausdorff distance, then we prove the existence of solutions of some shape optimization for elliptic equations.

Related

• Existence of surfaces optimizing geometric and PDE shape functionals under reach constraint
• Computable Operations on Compact Subsets of Metric Spaces with Applications to Fréchet Distance and Shape Optimization
• A shape optimization problem on planar sets with prescribed topology
• Shape optimization problems involving nonlocal and nonlinear operators
• Spectral Optimization Problems