A further remark on the density estimate for degenerate Allen-Cahn equations: Δ_p-type equations for 1

2025/07/26 by Zhang, Chilin
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2507.19820

Abstract

In this short remark on a previous paper \citeSZ25, we continue the study of Allen-Cahn equations associated with Ginzburg-Landau energies J(v,Ω)=∫_Ω\F(∇ v,v,x)+W(v,x)\dx, involving a Dirichlet energy F(ξ,τ,x)∼|ξ|^p and a degenerate double-well potential W(τ,x)∼(1-τ²)^m. In contrast to \citeSZ25, we remove all regularity assumptions on the Ginzburg-Landau energy. Then, with further assumptions that 1

Citations

• Density estimates for a (non)local variational model with degenerate double-well potential
• Density estimates for Ginzburg-Landau energies with degenerate double-well potentials
• Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials
• Density estimates for a nonlocal variational model with a degenerate double-well potential via the Sobolev inequality
• Density estimates for degenerate double-well potentials

Related

• Density estimates for Ginzburg-Landau energies with degenerate double-well potentials
• On stable solutions to the Allen-Cahn equation with bounded energy density in ℝ⁴
• Degenerate Kolmogorov equations and ergodicity for the stochastic Allen-Cahn equation with logarithmic potential
• Density estimates for degenerate double-well potentials
• On A_p weights and the Landau equation