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
\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:
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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
Robert Stegliński, “Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian”, Forum Mathematicum, 33:2 (2021), 465
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
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
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
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
Hadiji R., Baraket S., Yazidi H., “The Effect of a Discontinuous Weight For a Critical Sobolev Problem”, Appl. Anal., 97:14 (2018), 2544–2553
Cianchi A., Ferone V., Nitsch C., Trombetti C., “Balls minimize trace constants in BV”, J. Reine Angew. Math., 725 (2017), 41–61
Edward J., Hudson S., Leckband M., “Minimal Potential Results For Schrodinger Equations With Neumann Boundary Conditions”, Forum Math., 29:6 (2017), 1337–1348
Kuznetsov N., Nazarov A., “Sharp Constants in the Poincaré, Steklov and Related Inequalities (a Survey)”, Mathematika, 61:2 (2015), 328–344
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
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
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
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
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
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
de Valeriola S., Willem M., “On Some Quasilinear Critical Problems”, Adv. Nonlinear Stud., 9:4 (2009), 825–836
Nazarov A.I., “Dirichlet and Neumann problems to critical Emden-Fowler type equations”, J. Global Optim., 40:1-3 (2008), 289–303
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