Local approximations by solutions hypoelliptic equations, and removable singularities
type: Item
instance of: scholarly article
title: Local approximations by solutions hypoelliptic equations, and removable singularities
zbMATH Open document ID: 0985.35014
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: This paper deals with several properties of the solutions of quasihomogeneous hypoelliptic linear differential operators with constant coefficients. The author introduces the functional spaces \(U_p\subset L_p\), the anisotropic Campanato classes \(C_p\), the anisotrophic Morrey class \(W_p\). In Theorems 1-3, relations of the type \(U_p\subset C_p\), \(1\leq p< \infty\), \(U_p= W_p\) are shown. Under some conditions it is announced that for homogeneous elliptic operators of order \(m>1\), \(1\leq p\leq \infty\) the class \(U_p\) coincides with the Hölder-Zygmund class \(\Lambda^s\). In Theorems 6, 7, removability of the singularities of solutions to the equation \(P(D)u=0\) are established. No proofs or sketches of the proofs are given.
reviewed by: Peter R. Popivanov
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1557739
zbMATH Keywords: anisotropic Campanato classes
zbMATH Keywords: anisotrophic Morrey class
zbMATH Keywords: Hölder-Zygmund class
author: A. V. Pokrovskiĭ
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557739