Generalised Young Measures and characterisation of gradient Young Measures

2023/01/05 by Seneci, Tommaso
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.02154

Abstract

Given a function f∈ C(ℝ^d) of linear growth, we give a new way of representing accumulation points of ∫_Ωf(v_i(z))dμ(z), where μ∈ M⁺(Ω), and (v_i)_{i∈ ℕ}⊂ L¹(Ω,μ) is norm bounded. We call such representations "generalised Young Measures". With the help of the new representations, we then characterise these limits when they are generated by gradients, i.e. when v_i = Du_i for u_i∈ W^1,1(Ω,ℝ^m), via a set of integral inequalities.

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