Higher Sobolev Regularity of Convex Integration Solutions in Elasticity

2016/10/08 by Angkana Rüland, Rüland, Angkana, Christian Zillinger +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1610.02529

openalex publication_date 2016/10/08 · openalex created_date 2016/10/21 · openalex updated_date 2026/07/28

Abstract

In this article we discuss quantitative properties of convex integration solutions arising in problems modeling shape-memory materials. For a two-dimensional, geometrically linearized model case, the hexagonal-to-rhombic phase transformation, we prove the existence of convex integration solutions u with higher Sobolev regularity, i.e. there exists θ₀>0 such that ∇ u ∈ W^s,p_loc(ℝ²)∩ L^∞(ℝ²) for s∈(0,1), p∈(1,∞) with 0

Citations

• Fine phase mixtures as minimizers of energy

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