An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives

2020/03/18 by Hongjie Dong, Dong, Hongjie, Doyoon Kim +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2003.08000

openalex publication_date 2020/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend the previous result in [6] for unmixed L_p-estimates without weights.

Citations

• Weighted Inequalities for Maximal Operators: Linearization, Localization and Factorization
• L_p-estimates for time fractional parabolic equations in divergence form with measurable coefficients
• Weighted L_q(L_p)-estimate with Muckenhoupt weights for the diffusion-wave equations with time-fractional derivatives

Related

• Weighted estimates for time-fractional parabolic equations with VMO coefficients
• On weighted mixed-norm Sobolev estimates for some basic parabolic equations
• Sobolev estimates for fractional parabolic equations with space-time non-local operators
• L_p-estimates of the conormal derivative problem for parabolic equations with time measurable coefficients and A_p-weights
• Weighted mixed-norm L_p-estimates for elliptic and parabolic equations in non-divergence form with singular degenerate coefficients