On parabolic equations in one space dimension

N. V. Krylov

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4 Scopus citations

Abstract

Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main coefficient is assumed to be a bounded measurable function of (t, x) bounded away from 0. We also discuss upper and lower estimates of certain kind on the fundamental solutions of such equations.

Original languageEnglish (US)
Pages (from-to)644-664
Number of pages21
JournalCommunications in Partial Differential Equations
Volume41
Issue number4
DOIs
StatePublished - Mar 17 2015

Bibliographical note

Publisher Copyright:
© 2016 Taylor & Francis.

Keywords

  • Absence of a priori estimates
  • Estimates on the fundamental solutions
  • Sobolev classes

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