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

Previous article Next article Minimum Value for c in the Sobolev Inequality \| ³ \| c\| \|³ Gerald 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 ². 0780 for 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 Scholar2 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 Scholar3 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 Scholar4 R. Courant and, D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc. , New York, N. Y. , 1953xv+561 MR0065391 0053. 02805 Google Scholar5 E. Kamke, Differentialgleichungen Lösungsmethoden and Lösungen, Akademische Verlags, Leipzig, 1956 Google Scholar6 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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