Optimal regularity for the Signorini problem and its free boundary

DOI10.1007/s00222-015-0608-6zbMath1339.35345arXiv1310.2511OpenAlexW1598210624MaRDI QIDQ284620

John Andersson

Publication date: 18 May 2016

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.2511

zbMATH Keywords

Signorini problemfree boundary regularityLame systemoptimal regularity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) Free boundary problems for PDEs (35R35)

Related Items (10)

The variable coefficient thin obstacle problem: optimal regularity and regularity of the regular free boundary ⋮ The variable coefficient thin obstacle problem: Carleman inequalities ⋮ A minimization problem with free boundary related to a cooperative system ⋮ Optimal regularity for the thin obstacle problem with \(C^{0,\alpha }\) coefficients ⋮ On the measure and the structure of the free boundary of the lower dimensional obstacle problem ⋮ Shape optimisation with the level set method for contact problems in linearised elasticity ⋮ Monotonicity formulas for coupled elliptic gradient systems with applications ⋮ Higher regularity for the Signorini problem for the homogeneous, isotropic Lamé system ⋮ The thin obstacle problem: a survey ⋮ Sensitivity analysis of a Tresca-Type Problem leads to Signorini’s conditions

Cites Work

• Regularity for Signorini's problem in linear elasticity
• Positive harmonic functions vanishing on the boundary of certain domains in \(R^ n\).
• Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions
• Boundary estimates for solutions of the parabolic free boundary problem
• A homogeneity improvement approach to the obstacle problem
• Equilibrium points of a singular cooperative system with free boundary
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• Optimal regularity of lower dimensional obstacle problems
• Über Wachstumseigenschaften gewisser Klassen von subharmonischen Funktionen
• The smoothness of the free boundary for a class of vector-valued problems
• The structure of the free boundary for lower dimensional obstacle problems
• Further regularity for the signorini problem
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