A non-local one-phase free boundary problem from obstacle to cavitation

2018/10/10 by Yijing Wu, Wu, Yijing
Mathematics · #35R11 #35R35 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1810.05535

openalex publication_date 2018/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a one-phase free boundary problem of the minimizer of the energy J_γ(u)=(1)/(2)∫_{(B1ⁿ⁺¹)⁺}y^1-2s|∇ u(x,y)|²dxdy+∫_B₁ⁿ× \y=0\u^γdx, with constants 0

Citations

• Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian

Related

• Boundary Regularity for the Free Boundary in the One-phase Problem
• One-phase free-boundary problems with degeneracy
• A free boundary problem driven by boundary distance in the coincidence set
• The two-phase fractional obstacle problem
• On certain degenerate one-phase free boundary problems