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    Universal estimate of the gradient for parabolic equations

    166899_166899.pdf (116.2Kb)
    Access Status
    Open access
    Authors
    Dokuchaev, Nikolai
    Date
    2008
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Dokuchaev, Nikolai. 2008. Universal estimate of the gradient for parabolic equations. Journal of Physics A: Mathematical and Theorectical. 41 (21): pp. 1-12.
    Source Title
    Journal of Physics A: Mathematical and Theorectical
    DOI
    10.1088/1751-8113/41/21/215202
    ISSN
    17518113
    School
    Department of Mathematics and Statistics
    Remarks

    Copyright © 2008 IOP Institute of Physics

    URI
    http://hdl.handle.net/20.500.11937/16598
    Collection
    • Curtin Research Publications
    Abstract

    We suggest a modification of the estimate for weighted Sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the weight for the gradient. More precisely, we found the upper limit estimate that can be achieved by variations of the zero-order coefficient. As an example of applications, an asymptotic estimate was obtained for the gradient at initial time. The constant in the estimates is the same for all possible choices of the dimension, domain, time horizon and the coefficients of the parabolic equation. As an another example of application, existence and regularity results are obtained for parabolic equations with time delay for the gradient.

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