A Note on Linear Elliptic Systems on \R^d

2012/02/17 by Christoph Ortner, Ortner, Christoph, Endre Süli +2 · 5 citations
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1202.3970

openalex publication_date 2012/02/17 · arxiv created 2012/04/13 · arxiv updated 2012/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are concerned with the well-posedness of linear elliptic systems posed on ℝ^d. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite elasticity, however, our results are more generally applicable to translation-invariant problem posed on ℝ^d. We describe a variant of homogeneous Sobolev spaces, which are convenient for treating problems of this kind.

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