Fourth-order operators with unbounded coefficients in L¹ spaces

2024/07/15 by Federica Gregorio, Gregorio, Federica, Chiara Spina +3
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2407.10551

openalex publication_date 2024/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that operators of the form A=-a(x)²Δ², with suitable growth conditions on the coefficient a(x), generate analytic semigroups in L¹(ℝ^N). In particular, we deduce generation results for the operator A :=- (1+|x|²)^α Δ², 0≤α≤2. Moreover, we characterise the maximal domain of A in L¹(ℝ^N).

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