6533b836fe1ef96bd12a0a86

RESEARCH PRODUCT

Symmetry breaking in a constrained cheeger type isoperimetric inequality

Francesco Della PietraBarbara BrandoliniCristina TrombettiCarlo Nitsch

subject

Control and OptimizationOptimal shapeZero (complex analysis)Symmetry and asymmetryMeasure (mathematics)Sobolev inequalityCheeger inequalityCombinatoricsComputational MathematicsMathematics - Analysis of PDEsOptimization and Control (math.OC)Control and Systems EngineeringSettore MAT/05 - Analisi MatematicaFOS: MathematicsExponentSymmetry breakingIsoperimetric inequalitySymmetry (geometry)Constant (mathematics)Mathematics - Optimization and ControlAnalysis of PDEs (math.AP)Mathematics

description

We study the optimal constant in a Sobolev inequality for BV functions with zero mean value and vanishing outside a bounded open set. We are interested in finding the best possible embedding constant in terms of the measure of the domain alone. We set up an optimal shape problem and we completely characterize the behavior of optimal domains.

yearjournalcountryeditionlanguage
2015-01-01
10.1051/cocv/2014016http://hdl.handle.net/10447/493970