Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem

2025/07/30 by Dong, Hongjie, Jeon, Seongmin · 1 citation
#35B45 #35B65 #35K65 #35K67 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.22663

Abstract

In this paper, we study solutions u of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder Q₁⁺⊂ ℝⁿ⁺¹, where the coefficients are weighted by x_n^α, α∈(-∞,1). We establish higher-order boundary Schauder type estimates of x_n^αu under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with Hölder continuous coefficients.

Citations

• Schauder type estimates for degenerate or singular parabolic systems with partially DMO coefficients
• Higher order Schauder estimates for degenerate or singular parabolic equations
• Parabolic and elliptic equations with singular or degenerate coefficients: the Dirichlet problem
• Gradient estimates for Stokes systems with Dini mean oscillation coefficients
• The Pricing of Options and Corporate Liabilities

Cited by

• On some divergence-form singular elliptic equations with codimension-two boundary: L^p-estimates

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