Global estimates for quasilinear parabolic equations on Reifenberg flat\n domains and its applications to Riccati type parabolic equations with\n distributional data

2015/10/22 by Quoc‐Hung Nguyen, Nguyen, Quoc-Hung
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35K59 #Secondary 42B37

paper · pdf · doi:10.48550/arxiv.1511.06218

openalex publication_date 2015/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates\nfor gradients of solutions to the quasilinear parabolic equations:ν_t-
operatornamediv(A(x,t,
nabla u))=
operatornamediv(F), in a bounded\ndomain \Ω\× (0,T)\⊂\ℝ^N+1, under minimal regularity\nassumptions on the boundary of domain and on nonlinearity A. Then results\nyields existence of a solution to the Riccati type parabolic equations:ν_t-
operatornamediv(A(x,t,
nabla u))=|
nablaν|^q+
operatornamediv(F)+
mu, where q>1 and \μ is a bounded Radon\nmeasure.\n

Citations

• Solution of the Plateau problem for m-dimensional surfaces of varying topological type

Related

• Potential estimates and quasilinear parabolic equations with measure data
• Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains
• Global Lorentz and Lorentz-Morrey estimates below the natural exponent\n for quasilinear equations
• Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains,\n with applications to quasilinear Riccati type equations
• Lorentz-Morrey global bounds for singular quasilinear elliptic equations with measure data