Regularity of the free boundary for the two-phase Bernoulli problem
Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
2021CINECA IRIS Institutial research information system (University of Pisa)30 citationsDOIOpen Access PDF
Abstract
We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.
Topics & Concepts
MathematicsBernoulli's principleEigenvalues and eigenvectorsBoundary (topology)Dirichlet problemFree boundary problemDirichlet distributionDirichlet boundary conditionPhase (matter)Dirichlet eigenvalueMathematical analysisPure mathematicsBoundary value problemApplied mathematicsDirichlet's principleOrganic chemistryPhysicsEngineeringAerospace engineeringQuantum mechanicsChemistryAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsSpectral Theory in Mathematical Physics