Parabolic equations involving Bessel operators and singular integrals

2017/02/16 by Jorge J. Betancor, Betancor, Jorge J., Marta De León-Contreras +1
Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.04994

openalex publication_date 2017/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the evolution equation ∂_t u=Δ_μu+f and the corresponding Cauchy problem, where Δ_μ represents the Bessel operator ∂_x²+((1)/(4)-μ²)x^-2, for every μ>-1. We establish weighted and mixed weighted Sobolev type inequalities for solutions of Bessel parabolic equations. We use singular integrals techniques in a parabolic setting.

Citations

• On the existence of certain singular integrals
• On weighted mixed-norm Sobolev estimates for some basic parabolic equations

Related

• On weighted mixed-norm Sobolev estimates for some basic parabolic equations
• Hölder, Sobolev, weak-type and BMO estimates in mixed-norm with weights for parabolic equations
• Parabolic weighted Sobolev-Poincaré type inequalities
• Regularity theory for parabolic equations with singular degenerate coefficients
• Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces