Minimum Value for c in the Sobolev Inequality \| φ ³ \| c\| ∇ φ \|³

Previous article Next article Minimum Value for c in the Sobolev Inequality \| φ ³ \| c\| ∇ φ \|³Gerald RosenGerald Rosenhttps://doi.org/10.1137/0121004PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown that the minimum value for c is 4/3 √ 3 π ² .0780 for φ of function class C⁰ piecewise C² in real Euclidean 3-space.[1] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3), 13 (1959), 115–162 MR0109940 0088.07601 Google Scholar[2] Hiroshi Fujita and , Tosio Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal., 16 (1964), 269–315 10.1007/BF00276188 MR0166499 0126.42301 CrossrefISIGoogle Scholar[3] Hiroshi Fujita, On the existence and regularity of the steady-state solutions of the Navier-Stokes theorem, J. Fac. Sci. Univ. Tokyo Sect. I, 9 (1961), 59–102 (1961) MR0132307 0111.38502 Google Scholar[4] 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[5] E. Kamke, Differentialgleichungen Lösungsmethoden and Lösungen, Akademische Verlags, Leipzig, 1956 Google Scholar[6] M. A. Krasnoselskii˘, Positive solutions of operator equations, Translated from the Russian by Richard E. Flaherty; edited by LeoF. Boron, P. Noordhoff Ltd. Groningen, 1964, 381– MR0181881 0121.10604 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Nonlocal fractional system involving the fractional p, q-Laplacians and singular potentialsArabian Journal of Mathematics, Vol. 185 | 11 July 2022 Cross Ref Reverse conformally invariant Sobolev inequalities on the sphereJournal of Functional Analysis, Vol. 282, No. 4 | 1 Feb 2022 Cross Ref Functional Inequalities: Nonlinear Flows and Entropy Methods as a Tool for Obtaining Sharp and Constructive ResultsMilan Journal of Mathematics, Vol. 89, No. 2 | 25 October 2021 Cross Ref Energy asymptotics in the three-dimensional Brezis–Nirenberg problemCalculus of Variations and Partial Differential Equations, Vol. 60, No. 2 | 19 February 2021 Cross Ref Sobolev inequalities for fractional Neumann Laplacians on half spacesAdvances in Calculus of Variations, Vol. 14, No. 1 | 11 October 2018 Cross Ref Existence of infinitely many solutions for a nonlocal elliptic PDE 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