Gradient estimates of very weak solutions to general quasilinear elliptic equations

2022/02/11 by Sun‐Sig Byun, Byun, Sun-Sig, Minkyu Lim +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2202.05414

openalex publication_date 2022/02/11 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/01

Abstract

We establish a gradient estimate for a very weak solution to a quasilinear elliptic equation with a nonstandard growth condition, which is a natural generalization of the p-Laplace equation. We investigate the maximum extent for the gradient estimate to hold without imposing any regularity assumption on the nonlinearity other than basic structure assumptions. Our results also include a higher integrability result of the gradient and the existence for the very weak solutions to such nonlinear problems.

Related

• Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates
• Up-to-boundary pointwise gradient estimates for very singular quasilinear elliptic equations with mixed data
• Gradient Estimates for Solutions To Quasilinear Elliptic Equations with Critical Sobolev Growth and Hardy Potential
• Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms
• Gradient weighted estimates at the natural exponent for Quasilinear Parabolic equations