Ukrainian Mathematical Journal

, Volume 45, Issue 7, pp 1145–1157 | Cite as

Limiting behavior of the solutions to linear second-order parabolic equations

  • I. I. Skrypnik


We study the properties of solutions to parabolic equations in smooth cylindrical domains and establish the conditions for the existence of limiting nontangents andL2-limits ast → 0.


Parabolic Equation Cylindrical Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. L. Burkholder and R. F. Gundy, “Distribution function inequalities for the area integral,”Stud. Math.,44, No. 6, 527–544 (1972).Google Scholar
  2. 2.
    V. Yu. Shelepov, “On the limiting properties of the solutions to elliptic equations in many-dimensional regions representable as a difference of convex functions,”Mat. Sb.,133, No. 4, 446–468 (1987).Google Scholar
  3. 3.
    I. I. Skrypnik, “Limiting values of the solutions to linear second-order parabolic equations,”Ukr. Mat. Zh.,44, No. 10, 1433–1440 (1992).Google Scholar
  4. 4.
    I. M. Petrushko, “On boundary and initial conditions inL p,p > 1, for the solutions of the second-order parabolic equations,”Mat. Sb.,125, No. 4, 489–521 (1984).Google Scholar
  5. 5.
    E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • I. I. Skrypnik
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian Academy of SciencesDonetsk

Personalised recommendations