Neumann problems for nonlinear elliptic equations with L¹ data

2014/10/02 by Maria Francesca Betta, Betta, Maria Francesca, Olivier Guibé +3
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.1410.0660

openalex publication_date 2014/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is \begincases -Δ_p u -div (c(x)|u|^p-2u)) =f amp; in Ω,
( |∇ u|^p-2∇ u+ c(x)|u|^p-2u )⋅\underline n=0 amp; on ∂ Ω , \endcases when f is just a summable function. Our approach allows also to deduce a stability result for renormalized solutions and an existence result for operator with a zero order term.

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