Hölder regularity of solutions of degenerate parabolic equations of general dimension

2024/12/01 by Jang, Hyo Seok, Lee, Ki-Ahm · 1 citation
#35B65 #35K65 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.00675

Abstract

We establish the Alexandroff-Bakelman-Pucci estimate, the Harnack inequality, the Hölder regularity and the Schauder estimates to a class of degenerate parabolic equations of non-divergence form in all dimensions Lu:= u_t -Lu= u_t -(x a₁₁ u_xx +2√(x) ∑_j=2ⁿ a_1j u_{x yj} + ∑_i,j=2ⁿ a_ij u_{yi yj} + b₁ u_x +∑_j=2ⁿ b_j u_yj ) =g on \(x ≥ 0, y=(y₂,…, y_n) ∈ ℝ^n-1\), with bounded measurable coefficients.

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• Boundary Estimates for the Monge-Ampère Equation in the Polygons with Guillemin Boundary Conditions

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