Previous article Next article Pointwise Bounds for Solutions of the First Initial-Boundary Value Problem for Parabolic EquationsV. G. SigillitoV. G. Sigillitohttps://doi.org/10.1137/0114084PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] F. Bellar , Masters Thesis , Pointwise bounds in elliptic and parabolic partial differential equations , Doctoral dissertation , University of Maryland, College Park , 1961 0152.30203 Google Scholar[2] Edwin F. Beckenbach and , Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Bd. 30, Springer-Verlag, Berlin, 1961xii+198 MR0158038 0097.26502 CrossrefGoogle Scholar[3] J. H. Bramble and , L. E. Payne, Bounds for solutions of second-order elliptic partial differential equations, Contributions to Differential Equations, 1 (1963), 95–127 MR0163049 0141.09801 Google Scholar[4] J. H. Bramble and , L. E. Payne, Inequalities for solutions of mixed boundary value problems for elastic plates, J. Res. Nat. Bur. Standards Sect. B, 68B (1964), 75–92 MR0178619 0125.15006 CrossrefGoogle Scholar[5] R. Courant and , D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953xv+561 MR0065391 0053.02805 Google Scholar[6] F. G. Dressel, The fundamental solution of the parabolic equation, Duke Math. J., 7 (1940), 186–203 10.1215/S0012-7094-40-00711-6 MR0003340 0024.31702 CrossrefGoogle Scholar[7] G. Faber, Beweis dass unter aller homogenen Membranen von gleicher Fläche und gleicher Spannung die Kreisformige den tiefsten Grundton gibt, Bayer. Akad. Wiss. Math.-Natur. Kl. S.-B., (1923), 273– Google Scholar[8] Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall Inc., Englewood Cliffs, N.J., 1964xiv+347 MR0181836 0144.34903 Google Scholar[9] E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Math. Ann., 94 (1924), 97– 10.1007/BF01208645 CrossrefGoogle Scholar[10] Marcel Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Math., 81 (1949), 1–223 MR0030102 0033.27601 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Priori Inequalities and the Direchlet Problem for a Pseudo-Parabolic EquationVincent G. Sigillito17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 7, No. 2AbstractPDF (494 KB)A review of least-squares methods for solving partial differential equationsInternational Journal for Numerical Methods in Engineering, Vol. 10, No. 5 Cross Ref Complete Families of Solutions for Parabolic Equations with Analytic CoefficientsDavid Colton17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 6, No. 6AbstractPDF (900 KB)Chapter 11 Convergence and Error Bounds Cross Ref Inequalities for membrane and Stekloff eigenvaluesJournal of Mathematical Analysis and Applications, Vol. 23, No. 1 Cross Ref On a Continuous Method of Approximating Solutions of the Heat EquationJournal of the ACM, Vol. 14, No. 4 Cross Ref A Priori Inequalities and Pointwise Bounds for Solutions of Fourth Order Elliptic Partial Differential EquationsV. G. Sigillito13 July 2006 | SIAM Journal on Applied Mathematics, Vol. 15, No. 5AbstractPDF (1356 KB)Inequalities for Nonlocal Parabolic and Higher Order Elliptic EquationsKarl Gustafson and Vincent Sigillito18 July 2006 | SIAM Review, Vol. 9, No. 3AbstractPDF (1199 KB)Pointwise Bounds for Solutions of Semilinear Parabolic EquationsVincent G. Sigillito18 July 2006 | SIAM Review, Vol. 9, No. 3AbstractPDF (444 KB) Volume 14, Issue 5| 1966SIAM Journal on Applied Mathematics History Submitted:26 November 1965Published online:13 July 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0114084Article page range:pp. 1038-1056ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics