FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2034697260> ?p ?o ?g. }

• W2034697260 endingPage "541" @default.
• W2034697260 startingPage "531" @default.
• W2034697260 abstract "Previous article Next article Inequalities for Nonlocal Parabolic and Higher Order Elliptic EquationsKarl Gustafson and Vincent SigillitoKarl Gustafson and Vincent Sigillitohttps://doi.org/10.1137/1009073PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. Agmon, , A. Douglis and , L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), 623–727 MR0125307 0093.10401 CrossrefISIGoogle Scholar[2] E. Amaldi and , E. Fermi, On the absorption and the diffusion of slow neutrons, Phys. Rev., 50 (1936), 899–928 10.1103/PhysRev.50.899 CrossrefGoogle Scholar[3] W. G. Bade and , R. S. Freeman, Closed extensions of the Laplace operator determined by a general class of boundary conditions, Pacific J. Math., 12 (1962), 395–410 MR0165132 0198.17403 CrossrefISIGoogle Scholar[4] Richard Beals, Nonlocal elliptic boundary value problems, Bull. Amer. Math. Soc., 70 (1964), 693–696 MR0167700 0125.33301 CrossrefISIGoogle Scholar[5] F. J. Bellar, Jr., Pointwise bounds for the second initial-boundary value problem of parabolic type, Pacific J. Math., 19 (1966), 205–219 MR0206513 0152.30203 CrossrefISIGoogle Scholar[6] 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[7] Stefan Bergman and , M. Schiffer, Kernel functions and elliptic differential equations in mathematical physics, Academic Press Inc., New York, N. Y., 1953xiii+432 MR0054140 0053.39003 Google Scholar[8] Gaston Bertrand, La théorie des marées et les équations intégrales, Ann. Sci. École Norm. Sup. (3), 40 (1923), 151–258 MR1509251 CrossrefGoogle Scholar[9] Garrett Birkhoff, Albedo functions for elliptic equations, Boundary problems in differential equations, Univ. of Wisconsin Press, Madison, Wis, 1960, 163–178, Mathematics Research Center MR0145193 0136.09304 Google Scholar[10] J. H. Bramble and , B. E. Hubbard, Some higher order integral identities with application to bounding techniques, J. Res. Nat. Bur. Standards Sect. B, 65B (1961), 261–268 MR0132909 0104.34901 CrossrefISIGoogle Scholar[11] J. H. Bramble and , L. E. Payne, Bounds for derivatives in the Dirichlet problem for Poisson's equation, J. Soc. Indust. Appl. Math., 10 (1962), 370–380 10.1137/0110027 MR0155994 0113.08903 LinkISIGoogle Scholar[12] 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[13] J. H. Bramble and , L. E. Payne, Bounds in the Neumann problem for second order uniformly elliptic operators, Pacific J. Math., 12 (1962), 823–833 MR0146504 0111.09701 CrossrefISIGoogle Scholar[14] J. H. Bramble and , L. E. Payne, Some integral inequalities for uniformly elliptic operators, Contributions to Differential Equations, 1 (1963), 129–135 MR0163050 0141.09802 Google Scholar[15] J. H. Bramble and , L. E. Payne, Bounds for derivatives in elliptic boundary value problems, Pacific J. Math., 14 (1964), 777–782 MR0178230 0178.13003 CrossrefISIGoogle Scholar[16] 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[17] 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[18] F. E. Browder, Strongly elliptic systems of differential equationsContributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N. J., 1954, 15–51 MR0067306 0057.32901 Google Scholar[19] J. W. Calkin, Abstract symmetric boundary conditions, Trans. Amer. Math. Soc., 45 (1939), 369–442 MR1501997 0021.13802 CrossrefGoogle Scholar[20] J. B. Diaz, Upper and lower bounds for quadratic integrals, and a point, for solutions of linear boundary value problems, Boundary problems in differential equations, Univ. of Wisconsin Press, Madison, 1960, 47–83, Mathematics Research Center, Wisconsin MR0113053 0107.31102 Google Scholar[21] R. C. DiPrima and , R. Sani, Two papers on the convergence of the Galerkin method, Math. Rep., 63, Rensselaer Polytechnic Institute, Troy, New York, 1964 Google Scholar[22] 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[23] F. G. Dressel, The fundamental solution of the parabolic equation. II, Duke Math. J., 13 (1946), 61–70 10.1215/S0012-7094-46-01307-5 MR0015637 0061.22205 CrossrefISIGoogle Scholar[24] G. Faber, Beweis dass unten aller homogenen Membranen von gleicher Fläche und gleicher Spannung die Kreisförmige den tiefsten Grundton gibt, Sitz. bayer. Akad. Wiss., (1923), 169–172 Google Scholar[25] Gaetano Fichera, Methods of functional linear analysis in mathematical physics: “a priori” estimates for the solutions of boundary value problems, Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, vol. III, Erven P. Noordhoff N.V., Groningen, 1956, 216–228 MR0091441 0074.07804 Google Scholar[26] Gaetano Fichera, Su un principio di dualità per talune formole di maggiorazione relative alle equazioni differenziali, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8), 19 (1955), 411–418 (1956) MR0079705 0071.31801 Google Scholar[27] Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall Inc., Englewood Cliffs, N.J., 1964xiv+347 MR0181836 0144.34903 Google Scholar[28] Bernard Friedman, Principles and techniques of applied mathematics, John Wiley & Sons Inc., New York, 1956, 174–190 MR0079181 0072.12806 Google Scholar[29] Karl Gustafson, A perturbation lemma, Bull. Amer. Math. Soc., 72 (1966), 334–338 MR0187101 0148.38204 CrossrefISIGoogle Scholar[30] Karl Gustafson, Stability inequalities for semimonotonically perturbed nonhomogeneous boundary problems, SIAM J. Appl. Math., 15 (1967), 368–391, See also A priori bounds with application to integrodifferential boundary problems, Tech. Note BN-389, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Maryland, 1965 10.1137/0115034 MR0216125 0152.11004 LinkISIGoogle Scholar[31] Günter Hellwig, Partial differential equations: An introduction, Translated by E. Gerlach, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964xiii+265 MR0173071 0133.35701 Google Scholar[32] Fritz John, Plane waves and spherical means applied to partial differential equations, Interscience Publishers, New York-London, 1955viii+172, Interscience Tracts no. 2 MR0075429 0067.32101 Google Scholar[33] O. D. Kellogg, Foundations of Potential Theory, Dover, New York, 1953 0053.07301 Google Scholar[34] E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Math. Ann., 94 (1925), 97–100, See also Uber Minimaleigenschaften der Kugel in drei und mehr Dimensionen, Acta Comm. Univ. Tartu (Dorpat), A9 (1926), p. 1 10.1007/BF01208645 MR1512244 CrossrefGoogle Scholar[35] R. Lattès and , J.-L. Lions, Sur une classe de problèmes aux limites intervenant en physique de réacteursSymposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integro-Differential Equations (Rome), Birkhäuser, Basel, 1960, 48–88 MR0158567 0123.07602 Google Scholar[36] Carlo Miranda, Equazioni alle derivate parziali di tipo ellittico, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 2, Springer-Verlag, Berlin, 1955viii+222 MR0087853 0065.08503 Google Scholar[37] Philip M. Morse and , Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York, 1953, 267– MR0059774 0051.40603 Google Scholar[38] Farouk M. Odeh, On the integrodifferential equations of the nonlocal theory of superconductivity, J. Mathematical Phys., 5 (1964), 1168–1182 10.1063/1.1704222 MR0210381 CrossrefISIGoogle Scholar[39] L. E. Payne, Bounds in the Cauchy problem for the Laplace equation, Arch. Rational Mech. Anal., 5 (1960), 35–45 (1960) MR0110875 0094.29801 CrossrefGoogle Scholar[40] L. E. Payne, Inequalities for eigenvalues of membranes and plates, J. Rational Mech. Anal., 4 (1955), 517–529 MR0070834 0064.34802 ISIGoogle Scholar[41] L. E. Payne and , H. F. Weinberger, Bounds for solutions of second order elliptic equations in terms of arbitrary vector fields, Arch. Rational Mech. Anal., 20 (1965), 95–106 10.1007/BF00284612 MR0192174 0135.15401 CrossrefGoogle Scholar[42] L. E. Payne and , H. F. Weinberger, Lower bounds for vibration frequencies of elastically supported membranes and plates, J. Soc. Indust. Appl. Math., 5 (1957), 171–182 10.1137/0105012 MR0092431 0083.19406 LinkISIGoogle Scholar[43] L. E. Payne and , H. F. Weinberger, New bounds for solutions of second order elliptic partial differential equations, Pacific J. Math., 8 (1958), 551–573 MR0104047 0093.10901 CrossrefGoogle Scholar[44] Åke Pleijel, Remarks on Courant's nodal line theorem, Comm. Pure Appl. Math., 9 (1956), 543–550 MR0080861 0070.32604 CrossrefISIGoogle Scholar[45] G. Pólya and , G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, no. 27, Princeton University Press, Princeton, N. J., 1951xvi+279 MR0043486 0044.38301 CrossrefGoogle Scholar[46] Marcel Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Math., 81 (1949), 1–223 MR0030102 0033.27601 CrossrefISIGoogle Scholar[47] D. Sadowska, Sur une équation intégro-différentielle de la théorie de la conductibilité, Ann. Polon. Math., 7 (1959), 81–92 MR0110004 0111.10501 CrossrefGoogle Scholar[48] Philip W. Schaefer, On the Cauchy problem for an elliptic system, Arch. Rational Mech. Anal., 20 (1965), 391–412 10.1007/BF00282360 MR0192176 0144.15101 CrossrefGoogle Scholar[49] V. G. Sigillito, A priori inequalities and pointwise bounds for solutions of certain elliptic and parabolic boundary value problems, TG-722, Applied Physics Laboratory, The Johns Hopkins University, Silver Spring, Maryland, 1965 Google Scholar[50] V. G. Sigillito, Pointwise bounds for solutions of the first initial-boundary value problem for parabolic equations, SIAM J. Appl. Math., 14 (1966), 1038–1056 10.1137/0114084 MR0206515 0145.35802 LinkISIGoogle Scholar[51] V. G. Sigillito, On a continuous method of approximating solutions of the heat equation, J. Assoc. Comput. Mach., 14 (1967), 732–741 MR0234652 0155.20904 CrossrefISIGoogle Scholar[52] George N. Trytten, Pointwise bounds for solutions of the Cauchy problem for elliptic equations, Arch. Rational Mech. Anal., 13 (1963), 222–244 10.1007/BF01262694 MR0149060 0115.08602 CrossrefISIGoogle Scholar[53] H. F. Weinberger, Symmetrization in uniformly elliptic problemsStudies in mathematical analysis and related topics, Stanford Univ. Press, Stanford, Calif., 1962, 424–428, Essays in honor of G. Pólya MR0145191 0123.07202 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails 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)Pointwise Bounds for Solutions of Semilinear Parabolic EquationsVincent G. Sigillito18 July 2006 | SIAM Review, Vol. 9, No. 3AbstractPDF (444 KB)Stability Inequalities for Semimonotonically Perturbed Nonhomogeneous Boundary ProblemsKarl Gustafson13 July 2006 | SIAM Journal on Applied Mathematics, Vol. 15, No. 2AbstractPDF (1886 KB) Volume 9, Issue 3| 1967SIAM Review History Submitted:09 November 1966Published online:18 July 2006 InformationCopyright © 1967 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1009073Article page range:pp. 531-541ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics" @default.
• W2034697260 created "2016-06-24" @default.
• W2034697260 creator A5046705270 @default.
• W2034697260 creator A5063717434 @default.
• W2034697260 date "1967-07-01" @default.
• W2034697260 modified "2023-10-09" @default.
• W2034697260 title "Inequalities for Nonlocal Parabolic and Higher Order Elliptic Equations" @default.
• W2034697260 cites W1180226343 @default.
• W2034697260 cites W1936358016 @default.
• W2034697260 cites W1964638403 @default.
• W2034697260 cites W1972432877 @default.
• W2034697260 cites W1986606841 @default.
• W2034697260 cites W1988342626 @default.
• W2034697260 cites W1994117304 @default.
• W2034697260 cites W1998251440 @default.
• W2034697260 cites W2014746305 @default.
• W2034697260 cites W2024386992 @default.
• W2034697260 cites W2028845451 @default.
• W2034697260 cites W2029894358 @default.
• W2034697260 cites W2043704875 @default.
• W2034697260 cites W2062815611 @default.
• W2034697260 cites W2063282823 @default.
• W2034697260 cites W2066830498 @default.
• W2034697260 cites W2067195515 @default.
• W2034697260 cites W2068300478 @default.
• W2034697260 cites W2073370369 @default.
• W2034697260 cites W2074021362 @default.
• W2034697260 cites W2080370876 @default.
• W2034697260 cites W2082142907 @default.
• W2034697260 cites W2082954523 @default.
• W2034697260 cites W2087264112 @default.
• W2034697260 cites W2123362904 @default.
• W2034697260 cites W2294808609 @default.
• W2034697260 cites W2316118222 @default.
• W2034697260 cites W2334448129 @default.
• W2034697260 cites W2562800485 @default.
• W2034697260 cites W4211157405 @default.
• W2034697260 cites W4240357387 @default.
• W2034697260 doi "https://doi.org/10.1137/1009073" @default.
• W2034697260 hasPublicationYear "1967" @default.
• W2034697260 type Work @default.
• W2034697260 sameAs 2034697260 @default.
• W2034697260 citedByCount "0" @default.
• W2034697260 crossrefType "journal-article" @default.
• W2034697260 hasAuthorship W2034697260A5046705270 @default.
• W2034697260 hasAuthorship W2034697260A5063717434 @default.
• W2034697260 hasConcept C10138342 @default.
• W2034697260 hasConcept C134306372 @default.
• W2034697260 hasConcept C162324750 @default.
• W2034697260 hasConcept C182306322 @default.
• W2034697260 hasConcept C186867907 @default.
• W2034697260 hasConcept C28826006 @default.
• W2034697260 hasConcept C33923547 @default.
• W2034697260 hasConcept C45555294 @default.
• W2034697260 hasConcept C93779851 @default.
• W2034697260 hasConceptScore W2034697260C10138342 @default.
• W2034697260 hasConceptScore W2034697260C134306372 @default.
• W2034697260 hasConceptScore W2034697260C162324750 @default.
• W2034697260 hasConceptScore W2034697260C182306322 @default.
• W2034697260 hasConceptScore W2034697260C186867907 @default.
• W2034697260 hasConceptScore W2034697260C28826006 @default.
• W2034697260 hasConceptScore W2034697260C33923547 @default.
• W2034697260 hasConceptScore W2034697260C45555294 @default.
• W2034697260 hasConceptScore W2034697260C93779851 @default.
• W2034697260 hasIssue "3" @default.
• W2034697260 hasLocation W20346972601 @default.
• W2034697260 hasOpenAccess W2034697260 @default.
• W2034697260 hasPrimaryLocation W20346972601 @default.
• W2034697260 hasRelatedWork W2042572051 @default.
• W2034697260 hasRelatedWork W2047131671 @default.
• W2034697260 hasRelatedWork W2146071439 @default.
• W2034697260 hasRelatedWork W2181432034 @default.
• W2034697260 hasRelatedWork W2544961282 @default.
• W2034697260 hasRelatedWork W2741316444 @default.
• W2034697260 hasRelatedWork W2905264121 @default.
• W2034697260 hasRelatedWork W3007838749 @default.
• W2034697260 hasRelatedWork W3188684596 @default.
• W2034697260 hasRelatedWork W4237951173 @default.
• W2034697260 hasVolume "9" @default.
• W2034697260 isParatext "false" @default.
• W2034697260 isRetracted "false" @default.
• W2034697260 magId "2034697260" @default.
• W2034697260 workType "article" @default.