Elliptic problems involving the 1--Laplacian and a singular lower order term

2017/11/18 by De Cicco, Cicco, De, Giachetti +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.06812

openalex publication_date 2017/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the Dirichlet problem for an equation involving the 1--Laplacian operator Δ₁ u and having a singular term of the type (f(x))/(u^γ). Here f∈ L^N(Ω) is nonnegative, 00 a.e., the solution satisfies those features that might be expected as well as a uniqueness result. We also give explicit 1--dimensional examples that show that, in general, uniqueness does not hold. We remark that the Anzellotti theory of L^∞--divergence--measure vector fields must be extended to deal with this equation.

Citations

• On a singular nonlinear elliptic boundary-value problem

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