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Mapping Properties of One Class of Quasielliptic Operators

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Mathematics and Computing (ICMC 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 655))

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Abstract

The paper is devoted to the theory of quasielliptic operators. We consider scalar and homogeneous quasielliptic operators \(\mathcal{L}(D_x)\) with lower terms in the whole space \({\mathbb R}^n\). Our aim is to study mapping properties of these operators in weighted Sobolev spaces. We introduce a special scale of weighted Sobolev spaces \(W^l_{p,q,\sigma }({\mathbb R}^n)\). These spaces coincide with known spaces of Sobolev type for some parameters l, q, \(\sigma \). We investigate mapping properties of the operators \(\mathcal{L}(D_x)\) in the spaces \(W^l_{p,q,\sigma }({\mathbb R}^n)\). 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.

G. Demidenko—The work is supported in part by the Program of the Presidium of the Russian Academy of Sciences (project no. 0314-2015-0011).

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Acad. Koptyug Avenue 4, 630090, Novosibirsk, Russia

    Gennadii Demidenko

  2. Novosibirsk State University, Pirogov Street 2, 630090, Novosibirsk, Russia

    Gennadii Demidenko

Authors
  1. Gennadii Demidenko
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Correspondence to Gennadii Demidenko .

Editor information

Editors and Affiliations

  1. Haldia Institute of Technology, Haldia, India

    Debasis Giri

  2. University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  3. Freie Universität Berlin, Berlin, Germany

    Heinrich Begehr

  4. Fordham University, Bronx, New York, USA

    Mohammad S. Obaidat

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Demidenko, G. (2017). Mapping Properties of One Class of Quasielliptic Operators. In: Giri, D., Mohapatra, R., Begehr, H., Obaidat, M. (eds) Mathematics and Computing. ICMC 2017. Communications in Computer and Information Science, vol 655. Springer, Singapore. https://doi.org/10.1007/978-981-10-4642-1_29

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  • DOI: https://doi.org/10.1007/978-981-10-4642-1_29

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4641-4

  • Online ISBN: 978-981-10-4642-1

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