Strongly elliptic operators with distributional coefficients

2003/01/13 by М. И. Нейман-заде, Neiman-zade, M. I., Андрей Андреевич Шкаликов +1
Computer Science · Mathematics · #35J30 #46E35 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0301126

openalex publication_date 2003/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study operators of the form L=∑_{|α|,|β|≤ n} D^αc_α,β D^β, x∈\mathbb Rⁿ provided that the coefficients of the main symbol corresponding to the indices |α|=|β|=m are continuous while the other ones are distributions. Assuming that the main symbol defines the strongly elliptic operator we find sufficient conditions for the coefficients c_α,β(x) which guarantee that the operator L is well defined. In particular, if c_α,β(x) belong to the spaces of multipliers from H₂^m-|α| to H₂^|β|-m then L defines a maximal sectorial operator in L₂(\mathbb Rⁿ). We also describe the spaces of multipliers.

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