On a class of divergence form linear parabolic equations with degenerate coefficients

2021/06/14 by Tuoc Phan, Phan, Tuoc, Tran, Hung Vinh
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2106.07637

openalex publication_date 2021/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in (-∞, T) × ℝ^d₊, where ℝ^d₊ = \x ∈ ℝ^d : x_d>0\ and T∈ (-∞, ∞] is given, and the diffusion matrices are the product of x_d and bounded uniformly elliptic matrices, which are degenerate at \x_d=0\. As such, our class of equations resembles well the corresponding class of degenerate viscous Hamilton-Jacobi equations. We obtain wellposedness results and regularity type estimates in some appropriate weighted Sobolev spaces for the solutions.

Citations

• User’s guide to viscosity solutions of second order partial differential equations

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