On linear elliptic and parabolic equations with growing drift in Sobolev spaces without weights

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Abstract

We consider uniformly elliptic and parabolic second-order equations with bounded zerothorder and bounded VMO leading coefficients and possibly growing first-order coefficients. We look for solutions which are summable to the pth power with respect to the usual Lebesgue measure along with their first and second-order derivatives with respect to the spatial variable. Bibliography: 12 titles.

Original languageEnglish (US)
Pages (from-to)75-90
Number of pages16
JournalJournal of Mathematical Sciences
Volume159
Issue number1
DOIs
StatePublished - May 2009

Bibliographical note

Funding Information:
Acknowledgments. This work was partially supported by NSF (grant No.

Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

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