Mapping properties of one class of quasielliptic operators

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Abstract

The paper is devoted to the theory of quasielliptic operators. We consider scalar and homogeneous quasielliptic operators L(Dx) with lower terms in the whole space ℝn . Our aim is to study mapping properties of these operators in weighted Sobolev spaces. We introduce a special scale of weighted Sobolev spaces Wl p,q,σ(ℝn). These spaces coincide with known spaces of Sobolev type for some parameters l, q, σ. We investigate mapping properties of the operators L(Dx) in the spaces Wp,q,σ(ℝn). We indicate conditions for unique solvability of quasielliptic equations and systems in these spaces, obtain estimates for solutions and formulate an isomorphism theorem for quasielliptic operators. To prove our results we construct special regularizers for quasielliptic operators.

Original languageEnglish
Title of host publicationMathematics and Computing - 3rd International Conference, ICMC 2017, Proceedings
PublisherSpringer-Verlag GmbH and Co. KG
Pages339-348
Number of pages10
ISBN (Print)9789811046414
DOIs
Publication statusPublished - 1 Jan 2017
Event3rd International Conference on Mathematics and Computing, ICMC 2017 - Haldia, India
Duration: 17 Jan 201721 Jan 2017

Publication series

NameCommunications in Computer and Information Science
Volume655
ISSN (Print)1865-0929

Conference

Conference3rd International Conference on Mathematics and Computing, ICMC 2017
CountryIndia
CityHaldia
Period17.01.201721.01.2017

Keywords

  • Isomorphism
  • Quasielliptic operators
  • Weighted Sobolev spaces

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