On a class of elliptic free boundary problems with multiple solutions

DOI10.1007/s00030-021-00699-3zbMath1465.35419arXiv2003.05921OpenAlexW3160563574MaRDI QIDQ2028654

Perera, Kanishka

Publication date: 1 June 2021

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.05921

zbMATH Keywords

multiple nontrivial solutionsapproximation and variational methodsnondifferentiable energy functionals

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with fluid mechanics (35Q35) Free boundary problems for PDEs (35R35) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Related Items

An elliptic problem of the Prandtl-Batchelor type with a singularity ⋮ On semilinear equations with free boundary conditions on stratified Lie groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic estimates for the plasma problem
• A non-linear eigenvalue problem: the shape at equilibrium of a confined plasma
• On the existence of convex classical solutions to a generalized Prandtl-Batchelor free boundary problem
• Some new monotonicity theorems with applications to free boundary problems.
• Higher critical points in an elliptic free boundary problem
• On the existence of convex classical solutions to a generalized Prandtl-Batchelor free-boundary problem. II
• Dual variational methods in critical point theory and applications
• Existence and nondegeneracy of ground states in critical free boundary problems
• On steady laminar flow with closed streamlines at large Reynolds number
• A proposal concerning laminar wakes behind bluff bodies at large Reynolds number
• Remarks on a free Boundary Value Problem Arising in Plasma Physics
• Variational Formulas on Lipschitz Domains
• Quantitative bounds for subcritical semilinear elliptic equations