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

This article is cited in 20 scientific papers (total in 20 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
References:
Received: 30.11.2004
English version:
St. Petersburg Mathematical Journal, 2006, Volume 17, Issue 5, Pages 773–796
DOI: https://doi.org/10.1090/S1061-0022-06-00929-0
Bibliographic databases:
Document Type: Article
Language: Russian
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
\Bibitem{DemNaz05}
\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
\mathnet{http://mi.mathnet.ru/aa708}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2241425}
\zmath{https://zbmath.org/?q=an:1113.49010}
\transl
\jour St. Petersburg Math. J.
\yr 2006
\vol 17
\issue 5
\pages 773--796
\crossref{https://doi.org/10.1090/S1061-0022-06-00929-0}
Linking options:
  • https://www.mathnet.ru/eng/aa708
  • https://www.mathnet.ru/eng/aa/v17/i5/p105
  • This publication is cited in the following 20 articles:
    1. D. E. Apushkinskaya, A. A. Arkhipova, A. I. Nazarov, V. G. Osmolovskii, N. N. Uraltseva, “A Survey of Results of St. Petersburg State University Research School on Nonlinear Partial Differential Equations. I”, Vestnik St.Petersb. Univ.Math., 57:1 (2024), 1  crossref
    2. D. V. Bystrov, A. I. Nazarov, “Zadacha Robena dlya kvazilineinykh uravnenii s kriticheskim rostom pravoi chasti”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 51, K yubileyu Niny Nikolaevny Uraltsevoi, Zap. nauchn. sem. POMI, 536, POMI, SPb., 2024, 126–139  mathnet
    3. Robert Stegliński, “Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian”, Forum Mathematicum, 33:2 (2021), 465  crossref
    4. N. S. Ustinov, “On the solvability of a critical semilinear problem with the spectral Neumann fractional Laplacian”, St. Petersburg Math. J., 33:1 (2022), 141–153  mathnet  crossref
    5. 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
    6. 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
    7. 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
    8. 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
    9. 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  scopus
    10. 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
    11. 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
    12. 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
    13. 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
    14. 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
    15. 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
    16. 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
    17. 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
    18. de Valeriola S., Willem M., “On Some Quasilinear Critical Problems”, Adv. Nonlinear Stud., 9:4 (2009), 825–836  crossref  mathscinet  zmath  isi
    19. 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
    20. 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
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