On Liouville’s Theorem for Biharmonic Functions
R.R. Huilgol · SIAM Journal on Applied Mathematics · 1971
Previous article Next article On Liouville's Theorem for Biharmonic FunctionsR. R. HuilgolR. R. Huilgolhttps://doi.org/10.1137/0120005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Murray H. Protter and , Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall Inc., Englewood Cliffs, N.J., 1967x+261 MR0219861 0153.13602 Google Scholar[2] J. H. Bramble and , L. E. Payne, Pointwise bounds in the first biharmonic boundary value problem, J. Math. and Phys., 42 (1963), 278–286 MR0159135 0168.37003 CrossrefISIGoogle Scholar[3] M. J. Turteltaub and , Eli Sternberg, Elastostatic uniqueness in the half-space, Arch. Rational Mech. Anal., 24 (1967), 233–242 MR0207276 0145.44905 CrossrefISIGoogle Scholar[4] R. J. Duffin and , Walter Noll, On exterior boundary value problems in linear elasticity, Arch. Rational Mech. Anal., 2 (1958), 191–196 10.1007/BF00277928 MR0098496 0088.16402 CrossrefISIGoogle Scholar[5] R. J. Duffin, Continuation of biharmonic functions by reflection, Duke Math. J., 22 (1955), 313–324 10.1215/S0012-7094-55-02233-X MR0079105 0064.35201 CrossrefISIGoogle Scholar[6] Alfred Huber, On the reflection principle for polyharmonic functions, Comm. Pure Appl. Math., 9 (1956), 471–478 MR0085355 0071.10301 CrossrefISIGoogle Scholar[7] R. Courant and , D. Hilbert, Methods of mathematical physics. Vol. II: Partial differential equations, (Vol. II by R. Courant.), Interscience Publishers (a division of John Wiley & Sons), New York-Lon don, 1962xxii+830 MR0140802 0099.29504 Google Scholar[8] R. J. Knops, Uniqueness for the whole space in classical elasticity, J. London Math. Soc., 39 (1964), 708–712 MR0166986 0133.18005 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energiesArchiv der Mathematik, Vol. 111, No. 3 | 9 May 2018 Cross Ref Compactness results for sequences of approximate biharmonic mapsPacific Journal of Mathematics, Vol. 276, No. 1 | 1 July 2015 Cross Ref A form of classical Liouville theorem for polyharmonic functionsHiroshima Mathematical Journal, Vol. 30, No. 2 | 1 Jan 2000 Cross Ref Saint-Venant's principle on unbounded regionsProceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 115, No. 3-4 | 14 November 2011 Cross Ref Liouville theorems for linear elliptic systemsProceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 94, No. 3-4 | 14 November 2011 Cross Ref ON ENTIRE SOLUTIONS IN SOME NONLINEAR FOURTH ORDER ELLIPTIC EQUATIONSNonlinear Phenomena in Mathematical Sciences | 1 Jan 1982 Cross Ref Liouville theorems for elliptic systems and nonlinear equations of fourth orderProceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 91, No. 3-4 | 14 November 2011 Cross Ref Liouville theorems for a class of fourth order elliptic equationsProceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 86, No. 1-2 | 14 November 2011 Cross Ref A Liouville-Type Problem in Partial Differential EquationsKuang-Ho ChenSIAM Journal on Applied Mathematics, Vol. 23, No. 2 | 12 July 2006AbstractPDF (170 KB) Volume 20, Issue 1| 1971SIAM Journal on Applied Mathematics1-141 History Submitted:28 April 1970Published online:12 July 2006 InformationCopyright © 1971 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0120005Article page range:pp. 37-39ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics