Unilateral Problems for Quasilinear Operators with Fractional Riesz Gradients

2023/11/30 by Pedro Miguel Campos, Campos, Pedro Miguel, José Francisco Rodrigues +1 · 2 citations
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.18428

openalex publication_date 2023/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we develop the classical theory of monotone and pseudomonotone operators in the class of convex constrained Dirichlet-type problems involving fractional Riesz gradients in bounded and in unbounded domains Ω⊂ℝ^d. We consider the problem of finding u∈ K^s, such that, ∫_ℝ^d\boldsymbola(x,u,D^s u)⋅ D^s(v-u) dx+∫_Ωb(x,u,D^s u)(v-u) dx≥ 0 %⟨ F, v-u⟩ for all v∈ K^s. Here K^s⊂Λ^s,p₀(Ω) is a non-empty, closed and convex set of a fractional Sobolev type space Λ^s,p₀(Ω) with 0≤ s≤ 1 and 1

Cited by

• Fractional weighted Sobolev spaces associated to the Riesz fractional gradient
• Local boundary conditions in nonlocal hyperelasticity via heterogeneous horizons

Related

• On Fractional Musielak-Sobolev spaces and applications to nonlocal problems
• On a class of nonlocal problems with fractional gradient constraint
• Gradient estimates via Riesz potentials and fractional maximal operators for quasilinear elliptic equations with applications
• On nonlocal variational and quasi-variational inequalities with fractional gradient
• Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient