A note on the monotonicity formula of Caffarelli-Jerison-Kenig

DOI10.4171/RLM/673zbMath1297.49066MaRDI QIDQ2509475

Bozhidar Velichkov

Publication date: 28 July 2014

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

zbMATH Keywords

regularityfree boundaryPDEsCaffarelli-Jerison-Kenig monotonicity formulamultiphase optimization problems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) Free boundary problems for PDEs (35R35) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (5)

Two- and multi-phase quadrature surfaces ⋮ An anisotropic monotonicity formula, with applications to some segregation problems ⋮ Regularity of the optimal sets for the second Dirichlet eigenvalue ⋮ Free boundary regularity for a multiphase shape optimization problem ⋮ Regularity of the free boundary for the two-phase Bernoulli problem

Cites Work

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• Nodal domains and spectral minimal partitions
• Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions
• Some new monotonicity theorems with applications to free boundary problems.
• On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae
• Lipschitz continuity of state functions in some optimal shaping
• An optimal partition problem related to nonlinear eigenvalues.
• An optimal partition problem for eigenvalues
• Variational problems with two phases and their free boundaries
• A variational problem for the spatial segregation of reaction-diffusion systems

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