Nondegeneracy implies the existence of parametrized families of free boundaries

DOI10.1016/j.jde.2023.11.011OpenAlexW4388742589MaRDI QIDQ6144827

Lorenzo Cavallina

Publication date: 30 January 2024

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2023.11.011

zbMATH Keywords

free boundary problemimplicit function theoremshape derivativesoverdetermined problemnondegenerate critical pointsSerrin's overdetermined problem

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Second-order elliptic equations (35J15) Optimization of shapes other than minimal surfaces (49Q10) Free boundary problems for PDEs (35R35) Bifurcations in context of PDEs (35B32) PDEs in connection with control and optimization (35Q93) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25)

Cites Work

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• An overdetermined problem with non-constant boundary condition
• A general approach to Morse theory
• An existence result for a class of shape optimization problems
• Shape variation and optimization. A geometrical analysis
• Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities
• Hyperbolic solutions to Bernoulli's free boundary problem
• The simultaneous asymmetric perturbation method for overdetermined free boundary problems
• Existence and stability of solutions for a fourth order overdetermined problem
• Structure of shape derivatives
• Morse theory and a non-linear generalization of the Dirichlet problem
• A symmetry problem in potential theory
• Nontrivial solutions to Serrin's problem in annular domains
• Linear stability estimates for Serrin's problem via a modified implicit function theorem
• On a two-phase Serrin-type problem and its numerical computation
• Stability analysis of the two-phase torsional rigidity near a radial configuration
• Convexity of free boundaries with bernoulli type boundary condition
• The Morse lemma for Banach spaces
• Uniqueness theorems for surfaces in the large. I, II, III, IV, V

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