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Algebra i Analiz, 2005, Volume 17, Issue 5, Pages 105–140 (Mi aa708)  

This article is cited in 17 scientific papers (total in 17 papers)

Research Papers

On the existence of an extremal function in Sobolev embedding theorems with limit exponent

A. V. Demyanov, A. I. Nazarov

Saint-Petersburg State University

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English version:
St. Petersburg Mathematical Journal, 2006, 17:5, 773–796

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Received: 30.11.2004

Citation: A. V. Demyanov, A. I. Nazarov, “On the existence of an extremal function in Sobolev embedding theorems with limit exponent”, Algebra i Analiz, 17:5 (2005), 105–140; St. Petersburg Math. J., 17:5 (2006), 773–796

Citation in format AMSBIB
\by A.~V.~Demyanov, A.~I.~Nazarov
\paper On the existence of an extremal function in Sobolev embedding theorems with limit exponent
\jour Algebra i Analiz
\yr 2005
\vol 17
\issue 5
\pages 105--140
\jour St. Petersburg Math. J.
\yr 2006
\vol 17
\issue 5
\pages 773--796

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    This publication is cited in the following articles:
    1. A. V. Demyanov, A. I. Nazarov, “On solvability of Dirichlet problem to semilinear Schrödinger equation with singular potential”, J. Math. Sci. (N. Y.), 143:2 (2007), 2857–2868  mathnet  crossref  mathscinet  zmath
    2. Nazarov A.I., “Dirichlet and Neumann problems to critical Emden-Fowler type equations”, J. Global Optim., 40:1-3 (2008), 289–303  crossref  mathscinet  zmath  isi  elib  scopus
    3. de Valeriola S., Willem M., “On Some Quasilinear Critical Problems”, Adv. Nonlinear Stud., 9:4 (2009), 825–836  crossref  mathscinet  zmath  isi
    4. Leckband M., “A rearrangement based proof for the existence of extremal functions for the Sobolev-Poincaré inequality on $B^n$”, J. Math. Anal. Appl., 363:2 (2010), 690–696  crossref  mathscinet  zmath  isi  scopus
    5. Nazarov A.I., Reznikov A.B., “On the existence of an extremal function in critical Sobolev trace embedding theorem”, J. Funct. Anal., 258:11 (2010), 3906–3921  crossref  mathscinet  zmath  isi  elib  scopus
    6. Barbosa E.R., Montenegro M., “On the compactness problem of extremal functions to sharp Riemannian $L^p$-Sobolev inequalities”, J. Differential Equations, 249:4 (2010), 965–988  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Bouchez V., Van Schaftingen J., “Extremal functions in Poincaré-Sobolev inequalities for functions of bounded variation”, Nonlinear Elliptic Partial Differential Equations, Contemporary Mathematics, 540, 2011, 47–58  crossref  mathscinet  zmath  adsnasa  isi
    8. Cianchi A., “A Sharp Trace Inequality for Functions of Bounded Variation in the Ball”, Proc. R. Soc. Edinb. Sect. A-Math., 142:6 (2012), 1179–1191  crossref  mathscinet  zmath  isi  scopus
    9. Nazarov A.I., “On the Dirichlet Problem Generated by the Maz'Ya-Sobolev Inequality”, Calc. Var. Partial Differ. Equ., 49:1-2 (2014), 369–389  crossref  mathscinet  zmath  isi  elib  scopus
    10. Kuznetsov N., Nazarov A., “Sharp Constants in the Poincaré, Steklov and Related Inequalities (a Survey)”, Mathematika, 61:2 (2015), 328–344  crossref  mathscinet  zmath  isi  elib  scopus
    11. Cianchi A., Ferone V., Nitsch C., Trombetti C., “Balls minimize trace constants in BV”, J. Reine Angew. Math., 725 (2017), 41–61  crossref  mathscinet  zmath  isi
    12. Edward J., Hudson S., Leckband M., “Minimal Potential Results For Schrodinger Equations With Neumann Boundary Conditions”, Forum Math., 29:6 (2017), 1337–1348  crossref  mathscinet  zmath  isi  scopus
    13. Cianchi A., Ferone V., Nitsch C., Trombetti C., “Poincare Trace Inequalities in Bv(Bn) With Non-Standard Normalization”, J. Geom. Anal., 28:4 (2018), 3522–3552  crossref  mathscinet  zmath  isi  scopus
    14. Hadiji R., Baraket S., Yazidi H., “The Effect of a Discontinuous Weight For a Critical Sobolev Problem”, Appl. Anal., 97:14 (2018), 2544–2553  crossref  mathscinet  zmath  isi  scopus
    15. Hadiji R., Vigneron F., “Existence of Solutions of a Non-Linear Eigenvalue Problem With a Variable Weight”, J. Differ. Equ., 266:2-3 (2019), 1488–1513  crossref  mathscinet  zmath  isi  scopus
    16. Bazarbacha I., “The Effect of a Discontinuous Weight For a Critical Sobolev Problem”, Proc. Rom. Acad. Ser. A-Math. Phys., 21:4 (2020), 303–309  mathscinet  isi
    17. N. S. Ustinov, “O razreshimosti polulineinoi zadachi so spektralnym drobnym laplasianom Neimana i kriticheskoi pravoi chastyu”, Algebra i analiz, 33:1 (2021), 194–212  mathnet
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